diff --git a/src/app/features/galaxy-system/galaxy-system-scene.component.spec.ts b/src/app/features/galaxy-system/galaxy-system-scene.component.spec.ts
index e669b9b..dfd9092 100644
--- a/src/app/features/galaxy-system/galaxy-system-scene.component.spec.ts
+++ b/src/app/features/galaxy-system/galaxy-system-scene.component.spec.ts
@@ -423,7 +423,7 @@ describe('GalaxySystemSceneComponent camera-flight transitions', () => {
     const refocus = vi.spyOn(StarFieldRenderer.prototype, 'refocus');
     await advanceFrames(engine, 0.3);
 
-    component.routeResult.set({ stars: [{ id: SUN.id, name: 'Sol' }, { id: PROXIMA.id, name: 'Proxima Centauri' }], totalPc: 1.3, neededRangePc: null });
+    component.routeResult.set({ stars: [{ id: SUN.id, name: 'Sol' }, { id: PROXIMA.id, name: 'Proxima Centauri' }], totalPc: 1.3, neededRangePc: null, gaveUp: false });
     await advanceFrames(engine, 0.3);
 
     // As catalogue indices: the Sun is the first entry of STARS, Proxima the third.
@@ -473,7 +473,7 @@ describe('GalaxySystemSceneComponent camera-flight transitions', () => {
       expect(links.mock.calls[1][1]).not.toBe(links.mock.calls[0][1]);
 
       // A route re-chooses the drawn stars around its pins, and here they come out the same: no new graph.
-      component.routeResult.set({ stars: [{ id: SUN.id, name: 'Sol' }], totalPc: 0, neededRangePc: null });
+      component.routeResult.set({ stars: [{ id: SUN.id, name: 'Sol' }], totalPc: 0, neededRangePc: null, gaveUp: false });
       await advanceFrames(engine, 0.3);
       await settle();
       expect(links).toHaveBeenCalledTimes(2);
@@ -595,12 +595,12 @@ describe('GalaxySystemSceneComponent camera-flight transitions', () => {
   });
 
   it('shows the answer to the latest route asked for, whatever order the answers arrive in', async () => {
-    type Answer = { route: { stars: number[]; totalPc: number; longestHopPc: number } | null; neededRangePc: number | null };
+    type Answer = { route: { stars: number[]; totalPc: number; longestHopPc: number } | null; neededRangePc: number | null; gaveUp: boolean };
     const answers: Array<(answer: Answer) => void> = [];
     const component = fixture.componentInstance as unknown as {
       routing: { route(): Promise<Answer>; links(): Promise<Float32Array>; dispose(): void };
       routePending(): boolean;
-      routeResult(): { stars: { id: number }[] } | null;
+      routeResult(): { stars: { id: number }[]; gaveUp: boolean } | null;
       onRouteRequested(request: { fromId: number; toId: number; rangePc: number }): void;
     };
     component.routing = {
@@ -613,13 +613,19 @@ describe('GalaxySystemSceneComponent camera-flight transitions', () => {
     component.onRouteRequested({ fromId: SUN.id, toId: PROXIMA.id, rangePc: 2 });
     expect(component.routePending()).toBe(true);
 
-    answers[1]({ route: { stars: [SUN.id, PROXIMA.id], totalPc: 1.3, longestHopPc: 1.3 }, neededRangePc: null });
+    answers[1]({ route: { stars: [SUN.id, PROXIMA.id], totalPc: 1.3, longestHopPc: 1.3 }, neededRangePc: null, gaveUp: false });
     await flushAsync();
-    answers[0]({ route: { stars: [SUN.id, ALPHA_CENTAURI.id], totalPc: 1.34, longestHopPc: 1.34 }, neededRangePc: null });
+    answers[0]({ route: { stars: [SUN.id, ALPHA_CENTAURI.id], totalPc: 1.34, longestHopPc: 1.34 }, neededRangePc: null, gaveUp: false });
     await flushAsync();
 
     expect(component.routeResult()?.stars.map((star) => star.id)).toEqual([SUN.id, PROXIMA.id]);
     expect(component.routePending()).toBe(false);
+
+    // "It gave up" travels to the panel, which says something else for it than for "there is none".
+    component.onRouteRequested({ fromId: SUN.id, toId: ALPHA_CENTAURI.id, rangePc: 0.5 });
+    answers[2]({ route: null, neededRangePc: null, gaveUp: true });
+    await flushAsync();
+    expect(component.routeResult()).toMatchObject({ stars: [], gaveUp: true });
   });
 
   it('releases the routes panel when a route cannot be worked out, so it can be tried again', async () => {
diff --git a/src/app/features/galaxy-system/galaxy-system-scene.component.ts b/src/app/features/galaxy-system/galaxy-system-scene.component.ts
index 971993d..7a693b9 100644
--- a/src/app/features/galaxy-system/galaxy-system-scene.component.ts
+++ b/src/app/features/galaxy-system/galaxy-system-scene.component.ts
@@ -1528,7 +1528,7 @@ export class GalaxySystemSceneComponent implements AfterViewInit, OnDestroy {
     const request = ++this.routeRequest;
     this.routePending.set(true);
     void this.routing.route(fromId, toId, rangePc, ROUTE_RANGE_CEILING_PC).then(
-      ({ route, neededRangePc }) => {
+      ({ route, neededRangePc, gaveUp }) => {
         if (request !== this.routeRequest) {
           return;
         }
@@ -1536,7 +1536,8 @@ export class GalaxySystemSceneComponent implements AfterViewInit, OnDestroy {
         this.routeResult.set({
           stars: route ? route.stars.map((id) => ({ id, name: this.starsById.get(id)?.name ?? `Star ${id}` })) : [],
           totalPc: route?.totalPc ?? 0,
-          neededRangePc
+          neededRangePc,
+          gaveUp
         });
         this.jumpLinks?.setRoute(route?.stars ?? [], (id) => this.starsById.get(id));
       },
diff --git a/src/app/features/galaxy-system/routing-client.spec.ts b/src/app/features/galaxy-system/routing-client.spec.ts
index 2d05f31..314cbe4 100644
--- a/src/app/features/galaxy-system/routing-client.spec.ts
+++ b/src/app/features/galaxy-system/routing-client.spec.ts
@@ -73,7 +73,7 @@ describe('RoutingClient without a worker', () => {
   it('answers a route from the index it was given', async () => {
     const client = new RoutingClient(STARS, POSITIONS, index);
 
-    await expect(client.route(100, 104, 1.5, 8)).resolves.toEqual({ route: routeBetween(index, 100, 104, 1.5), neededRangePc: null });
+    await expect(client.route(100, 104, 1.5, 8)).resolves.toEqual({ route: routeBetween(index, 100, 104, 1.5).route, neededRangePc: null, gaveUp: false });
     client.dispose();
   });
 
@@ -143,8 +143,8 @@ describe('RoutingClient with a worker', () => {
     await expect(first).resolves.toHaveLength(6);
 
     const routeRequest = worker.requests[1];
-    worker.answer({ kind: 'route', requestId: routeRequest.requestId, route: null, neededRangePc: 4 });
-    await expect(route).resolves.toEqual({ route: null, neededRangePc: 4 });
+    worker.answer({ kind: 'route', requestId: routeRequest.requestId, route: null, neededRangePc: 4, gaveUp: false });
+    await expect(route).resolves.toEqual({ route: null, neededRangePc: 4, gaveUp: false });
     await flush();
 
     expect(worker.requests.map((request) => (request.kind === 'links' ? request.rangePc : request.kind))).toEqual([5, 'route', 8]);
@@ -161,14 +161,14 @@ describe('RoutingClient with a worker', () => {
     const widerRange = client.route(100, 104, 2.5, 8);
 
     expect(worker.requests).toHaveLength(1);
-    worker.answer({ kind: 'route', requestId: worker.requests[0].requestId, route: null, neededRangePc: 4 });
+    worker.answer({ kind: 'route', requestId: worker.requests[0].requestId, route: null, neededRangePc: 4, gaveUp: false });
 
     expect(await again).toEqual(await once);
     await flush();
     // The same two stars at another range is another question.
     expect(worker.requests.map((request) => request.rangePc)).toEqual([1.5, 2.5]);
-    worker.answer({ kind: 'route', requestId: worker.requests[1].requestId, route: null, neededRangePc: null });
-    await expect(widerRange).resolves.toEqual({ route: null, neededRangePc: null });
+    worker.answer({ kind: 'route', requestId: worker.requests[1].requestId, route: null, neededRangePc: null, gaveUp: false });
+    await expect(widerRange).resolves.toEqual({ route: null, neededRangePc: null, gaveUp: false });
     client.dispose();
   });
 
@@ -218,6 +218,16 @@ describe('RoutingClient with a worker', () => {
     client.dispose();
   });
 
+  it('hands on that the search gave up, along with the answer it did give', async () => {
+    const { client, worker } = clientWithFake();
+    const answer = client.route(100, 105, 1.5, 8);
+
+    worker.answer({ kind: 'route', requestId: worker.requests[0].requestId, route: null, neededRangePc: null, gaveUp: true });
+
+    await expect(answer).resolves.toEqual({ route: null, neededRangePc: null, gaveUp: true });
+    client.dispose();
+  });
+
   it('rejects a request the worker failed on, and goes on to the next', async () => {
     const { client, worker } = clientWithFake();
     const failing = client.route(100, 104, 1.5, 8).catch((error: unknown) => error);
@@ -240,7 +250,7 @@ describe('RoutingClient with a worker', () => {
 
     worker.fail();
 
-    await expect(route).resolves.toEqual({ route: routeBetween(index, 100, 104, 1.5), neededRangePc: null });
+    await expect(route).resolves.toEqual({ route: routeBetween(index, 100, 104, 1.5).route, neededRangePc: null, gaveUp: false });
     expect(Array.from(await graph)).toEqual([0, 0, 0, 1, 0, 0]);
     await expect(client.route(100, 105, 1.5, 8)).resolves.toMatchObject({ route: null });
     expect(worker.terminated).toBe(true);
diff --git a/src/app/features/galaxy-system/routing-client.ts b/src/app/features/galaxy-system/routing-client.ts
index 3677913..58bf63f 100644
--- a/src/app/features/galaxy-system/routing-client.ts
+++ b/src/app/features/galaxy-system/routing-client.ts
@@ -6,6 +6,8 @@ import { StarRecord } from '../../shared/models/star.model';
 export interface RouteAnswer {
   readonly route: Route | null;
   readonly neededRangePc: number | null;
+  /** True when the search gave up rather than ruling a route out; see `routeBetween`. */
+  readonly gaveUp: boolean;
 }
 
 /** A request dropped before it was sent, because a newer one of the same kind replaced it. */
@@ -104,7 +106,9 @@ export class RoutingClient {
 
   route(fromId: number, toId: number, rangePc: number, ceilingPc: number): Promise<RouteAnswer> {
     return this.ask({ kind: 'route', requestId: this.nextRequestId++, fromId, toId, rangePc, ceilingPc }).then((response) =>
-      response.kind === 'route' ? { route: response.route, neededRangePc: response.neededRangePc } : { route: null, neededRangePc: null }
+      response.kind === 'route'
+        ? { route: response.route, neededRangePc: response.neededRangePc, gaveUp: response.gaveUp }
+        : { route: null, neededRangePc: null, gaveUp: false }
     );
   }
 
diff --git a/src/app/features/hud/hud-dock.component.spec.ts b/src/app/features/hud/hud-dock.component.spec.ts
index 9018ecf..bee9dd5 100644
--- a/src/app/features/hud/hud-dock.component.spec.ts
+++ b/src/app/features/hud/hud-dock.component.spec.ts
@@ -253,6 +253,26 @@ describe('HudDockComponent', () => {
     expect(tab('Readout').getAttribute('aria-selected')).toBe('true');
   });
 
+  it('says the search gave up rather than that there is no route, when that is what happened', () => {
+    fixture.componentRef.setInput('routing', true);
+    fixture.componentRef.setInput('defaultTab', 'routes');
+    const summary = () => host().querySelector('[data-testid="route-summary"]')?.textContent?.replace(/\s+/g, ' ').trim() ?? '';
+
+    fixture.componentRef.setInput('routeResult', { stars: [], totalPc: 0, neededRangePc: null, gaveUp: true });
+    fixture.detectChanges();
+    expect(summary()).toBe('Too many stars to search at this range.');
+
+    // Having looked everywhere the range reaches is a different answer, and one that can be stated.
+    fixture.componentRef.setInput('routeResult', { stars: [], totalPc: 0, neededRangePc: null, gaveUp: false });
+    fixture.detectChanges();
+    expect(summary()).toContain('No chain of jumps up to');
+
+    // A range a chain was found at is worth offering whether or not anything shorter was ruled out.
+    fixture.componentRef.setInput('routeResult', { stars: [], totalPc: 0, neededRangePc: 6.4, gaveUp: true });
+    fixture.detectChanges();
+    expect(summary()).toBe('No route at this range. 6.40 pc would reach.');
+  });
+
   it('keeps what the Routes panel was set to across a trip to another tab', () => {
     setReadout();
     fixture.componentRef.setInput('routing', true);
diff --git a/src/app/features/hud/routes-panel.component.ts b/src/app/features/hud/routes-panel.component.ts
index 395b2b9..b7304fb 100644
--- a/src/app/features/hud/routes-panel.component.ts
+++ b/src/app/features/hud/routes-panel.component.ts
@@ -20,8 +20,10 @@ export interface RouteResult {
   /** The chain, departure first. Empty when there is no route at the range asked for. */
   readonly stars: readonly { id: number; name: string }[];
   readonly totalPc: number;
-  /** The shortest range that would open a route, where none was found at the one asked for. */
+  /** A range that would open a route, where none was found at the one asked for. */
   readonly neededRangePc: number | null;
+  /** True when the search gave up rather than showing there is no route at this range. */
+  readonly gaveUp: boolean;
 }
 
 export interface RouteRequest {
@@ -113,7 +115,11 @@ type Field = 'from' | 'to';
             </p>
           } @else {
             <p data-testid="route-summary" class="text-sm text-muted">
-              No route at this range.
+              @if (plotted.gaveUp && plotted.neededRangePc === null) {
+                Too many stars to search at this range.
+              } @else {
+                No route at this range.
+              }
               @if (plotted.neededRangePc !== null) {
                 <button
                   type="button"
@@ -122,7 +128,7 @@ type Field = 'from' | 'to';
                 >
                   {{ format(plotted.neededRangePc) }} would reach.
                 </button>
-              } @else {
+              } @else if (!plotted.gaveUp) {
                 No chain of jumps up to {{ format(maxRangePc) }} reaches it.
               }
             </p>
diff --git a/src/app/shared/astro/jump-links.spec.ts b/src/app/shared/astro/jump-links.spec.ts
index b070a93..54d251a 100644
--- a/src/app/shared/astro/jump-links.spec.ts
+++ b/src/app/shared/astro/jump-links.spec.ts
@@ -14,7 +14,7 @@ function index(points: StarPoint[]): StarNeighbourhood {
 
 describe('routeBetween', () => {
   it('walks the chain a hop at a time when that is all the range allows', () => {
-    const route = routeBetween(chain(5), 0, 4, 1.5);
+    const { route } = routeBetween(chain(5), 0, 4, 1.5);
 
     expect(route?.stars).toEqual([0, 1, 2, 3, 4]);
     expect(route?.totalPc).toBeCloseTo(4);
@@ -24,7 +24,7 @@ describe('routeBetween', () => {
   it('goes straight there when the range reaches, however many stars lie between', () => {
     // The direct crossing is never longer than a chain through anything — Euclid says so — so a
     // range that covers it makes it the answer, and the stars in between are just scenery.
-    const route = routeBetween(chain(5), 0, 4, 5);
+    const { route } = routeBetween(chain(5), 0, 4, 5);
 
     expect(route?.stars).toEqual([0, 4]);
     expect(route?.totalPc).toBeCloseTo(4);
@@ -33,7 +33,7 @@ describe('routeBetween', () => {
   it('picks the shorter of two ways round when neither is a straight line', () => {
     // 0 to 3 is 10 pc, out of a 6 pc range. Two ways round, both inside it: through 1, barely
     // off the line, or through 2, well off it. Shorter is what "the way there" means.
-    const route = routeBetween(
+    const { route } = routeBetween(
       index([
         { id: 0, x: 0, y: 0, z: 0 },
         { id: 1, x: 5, y: 0.5, z: 0 },
@@ -56,19 +56,19 @@ describe('routeBetween', () => {
       { id: 2, x: 20, y: 0, z: 0 }
     ]);
 
-    expect(routeBetween(split, 0, 2, 5)).toBeNull();
+    expect(routeBetween(split, 0, 2, 5)).toEqual({ route: null, gaveUp: false });
   });
 
   it('answers nothing for a star that is not there, or for going nowhere', () => {
     const line = chain(3);
 
-    expect(routeBetween(line, 0, 0, 2)).toBeNull();
-    expect(routeBetween(line, 0, 99, 2)).toBeNull();
-    expect(routeBetween(line, 0, 2, 0)).toBeNull();
+    expect(routeBetween(line, 0, 0, 2).route).toBeNull();
+    expect(routeBetween(line, 0, 99, 2).route).toBeNull();
+    expect(routeBetween(line, 0, 2, 0).route).toBeNull();
   });
 
   it('reports the longest hop, which is what the range has to cover', () => {
-    const route = routeBetween(
+    const { route } = routeBetween(
       index([
         { id: 0, x: 0, y: 0, z: 0 },
         { id: 1, x: 1, y: 0, z: 0 },
@@ -82,11 +82,31 @@ describe('routeBetween', () => {
     expect(route?.longestHopPc).toBeCloseTo(4);
   });
 
+  it('says it gave up rather than that there is no chain, once it has spent its budget', () => {
+    // Nothing reaches the island, but the crowd around the departure is larger than the budget, so
+    // the search stops without having looked everywhere the range reaches. Read as "no chain", that
+    // is a confident wrong answer — and the range search downstream would build on it.
+    const search = routeBetween(knotAndChain(), 0, ISLAND, 1.5);
+
+    expect(search.route).toBeNull();
+    expect(search.gaveUp).toBe(true);
+  });
+
+  it('reports a genuine dead end as one, having looked everywhere the range reaches', () => {
+    const split = index([
+      { id: 0, x: 0, y: 0, z: 0 },
+      { id: 1, x: 1, y: 0, z: 0 },
+      { id: 2, x: 20, y: 0, z: 0 }
+    ]);
+
+    expect(routeBetween(split, 0, 2, 5)).toEqual({ route: null, gaveUp: false });
+  });
+
   it('heads for the destination rather than exhausting a dense knot around the departure', () => {
     // The Gaia catalogue in miniature: a crowd around the departure, larger than the search's
     // budget, with the only way on a thin chain leading out of it. A search widening evenly from
     // the departure spends the budget on the crowd and never reaches the chain's far end.
-    const route = routeBetween(knotAndChain(), 0, CHAIN_END, 1.5);
+    const { route } = routeBetween(knotAndChain(), 0, CHAIN_END, 1.5);
 
     expect(route).not.toBeNull();
     expect(route!.stars[route!.stars.length - 1]).toBe(CHAIN_END);
@@ -95,24 +115,55 @@ describe('routeBetween', () => {
 });
 
 /**
- * 21 000 stars scattered through the 30 pc cube around the origin, about ten times the density
- * around the real Sun and more than a search's budget, with a chain a parsec a hop running along
- * x from the origin out through the crowd and on to 75 pc.
+ * 45 000 stars scattered through the 30 pc cube around the origin, twenty times the density around
+ * the real Sun and more than a search's budget, with a chain a parsec a hop running along x from
+ * the origin out through the crowd and on to 75 pc — and one star at 500 pc that nothing reaches.
  */
 const CHAIN_END = 75;
+const ISLAND = 999;
 function knotAndChain(): StarNeighbourhood {
   let seed = 7;
   const random = () => ((seed = (seed * 1103515245 + 12345) % 2147483648) / 2147483648) * 30 - 15;
-  const knot: StarPoint[] = Array.from({ length: 21000 }, (_, i) => ({ id: 1000 + i, x: random(), y: random(), z: random() }));
+  const knot: StarPoint[] = Array.from({ length: 45000 }, (_, i) => ({ id: 1000 + i, x: random(), y: random(), z: random() }));
   const chainOut: StarPoint[] = Array.from({ length: CHAIN_END }, (_, i) => ({ id: i + 1, x: i + 1, y: 0, z: 0 }));
-  return index([{ id: 0, x: 0, y: 0, z: 0 }, ...knot, ...chainOut]);
+  return index([{ id: 0, x: 0, y: 0, z: 0 }, ...knot, ...chainOut, { id: ISLAND, x: 500, y: 0, z: 0 }]);
+}
+
+/**
+ * 45 000 stars in a 10 pc cube — dense enough to stay one connected piece at half a parsec, where
+ * walking it costs more than a search's budget — with a chain a parsec a hop leaving its edge for
+ * 30 pc. Its cells are sized for the ranges asked of it, as the real catalogue's are for its own.
+ */
+const CROWD_CHAIN_END = 25;
+const CROWD_ISLAND = 999999;
+function crowdedKnot(): StarNeighbourhood {
+  let seed = 11;
+  const random = () => ((seed = (seed * 1103515245 + 12345) % 2147483648) / 2147483648) * 10 - 5;
+  const knot: StarPoint[] = Array.from({ length: 45000 }, (_, i) => ({ id: 1000 + i, x: random(), y: random(), z: random() }));
+  const chainOut: StarPoint[] = Array.from({ length: CROWD_CHAIN_END }, (_, i) => ({ id: i + 1, x: 5 + i + 1, y: 0, z: 0 }));
+  // One star nothing reaches, for the questions that have no answer.
+  return new StarNeighbourhood([{ id: 0, x: 0, y: 0, z: 0 }, ...knot, ...chainOut, { id: CROWD_ISLAND, x: 500, y: 0, z: 0 }], 0.5);
 }
 
 describe('minimumRangeBetween', () => {
   it('works out the range past a dense knot around the departure', () => {
     // Past the crowd the chain's hops of a parsec are the only way on, so a parsec is the
     // answer, to the half-step the panel rounds up to.
-    expect(minimumRangeBetween(knotAndChain(), 0, CHAIN_END, 8)).toBeCloseTo(1, 1);
+    expect(minimumRangeBetween(knotAndChain(), 0, CHAIN_END, 8).rangePc).toBeCloseTo(1, 1);
+  });
+
+  it('stops bisecting where a search gave up, and hands back a range that does work', () => {
+    // Below the chain's own hop of a parsec, the crowd is still one connected piece and larger than
+    // the budget, so those probes give up. Reading a give-up as "no chain at this range" is what
+    // used to report ranges up to 29% wider than needed, and went on paying for probes whose
+    // answers it could not use; the answer now is the narrowest range a chain was found at.
+    const knot = crowdedKnot();
+
+    const needed = minimumRangeBetween(knot, 0, CROWD_CHAIN_END, 2);
+
+    expect(needed.least).toBe(false);
+    expect(needed.rangePc).not.toBeNull();
+    expect(routeBetween(knot, 0, CROWD_CHAIN_END, needed.rangePc!).route).not.toBeNull();
   });
 
   it('names the shortest range that opens a way through', () => {
@@ -123,9 +174,9 @@ describe('minimumRangeBetween', () => {
       { id: 2, x: 5, y: 0, z: 0 }
     ]);
 
-    expect(minimumRangeBetween(stepped, 0, 2, 50)).toBeCloseTo(4);
-    expect(routeBetween(stepped, 0, 2, 4)).not.toBeNull();
-    expect(routeBetween(stepped, 0, 2, 3.99)).toBeNull();
+    expect(minimumRangeBetween(stepped, 0, 2, 50)).toEqual({ rangePc: expect.closeTo(4) as number, least: true });
+    expect(routeBetween(stepped, 0, 2, 4).route).not.toBeNull();
+    expect(routeBetween(stepped, 0, 2, 3.99).route).toBeNull();
   });
 
   it('prefers a longer way whose worst hop is shorter, since that is what the range pays for', () => {
@@ -139,8 +190,16 @@ describe('minimumRangeBetween', () => {
 
     const needed = minimumRangeBetween(both, 0, 3, 50);
 
-    expect(needed).toBeLessThan(10);
-    expect(routeBetween(both, 0, 3, needed!)).not.toBeNull();
+    expect(needed.rangePc).toBeLessThan(10);
+    expect(routeBetween(both, 0, 3, needed.rangePc!).route).not.toBeNull();
+  });
+
+  it('claims nothing about a ceiling its own search gave up on', () => {
+    // Nothing reaches the island at any range here, but the crowd spends the budget first, so the
+    // widest search proves nothing — and neither does the null it hands back.
+    const needed = minimumRangeBetween(crowdedKnot(), 0, CROWD_ISLAND, 0.5);
+
+    expect(needed).toEqual({ rangePc: null, least: false });
   });
 
   it('finds nothing when even the ceiling does not reach', () => {
@@ -149,7 +208,7 @@ describe('minimumRangeBetween', () => {
       { id: 1, x: 100, y: 0, z: 0 }
     ]);
 
-    expect(minimumRangeBetween(split, 0, 1, 50)).toBeNull();
+    expect(minimumRangeBetween(split, 0, 1, 50)).toEqual({ rangePc: null, least: true });
   });
 });
 
@@ -296,7 +355,7 @@ describe('jumpLinkSegments', () => {
 
     const drawn = new Set(linksDrawn(jumpLinkSegments(cloud, range), points));
 
-    const route = routeBetween(cloud, 0, 119, range);
+    const { route } = routeBetween(cloud, 0, 119, range);
     // Asserted, not guarded: a skipped body would let the two disagree unnoticed.
     expect(route).not.toBeNull();
     expect(route!.stars.length).toBeGreaterThan(2);
diff --git a/src/app/shared/astro/jump-links.ts b/src/app/shared/astro/jump-links.ts
index fca2f03..3f36c51 100644
--- a/src/app/shared/astro/jump-links.ts
+++ b/src/app/shared/astro/jump-links.ts
@@ -16,6 +16,21 @@
 
 import { StarNeighbourhood } from './star-neighbourhood';
 
+/** What a search found, and whether it looked everywhere the range reaches before answering. */
+export interface RouteSearch {
+  readonly route: Route | null;
+  /** True when the search spent its budget: "no route" then means "gave up", not "there is none". */
+  readonly gaveUp: boolean;
+}
+
+/** A range that opens a route, and whether anything shorter was actually ruled out. */
+export interface RangeSearch {
+  /** A range a chain was found at, or `null` where none was found up to the ceiling. */
+  readonly rangePc: number | null;
+  /** True when every shorter range was searched to exhaustion, so this is the least that works. */
+  readonly least: boolean;
+}
+
 /** A chain of stars from one to another, each hop within the range that was asked for. */
 export interface Route {
   /** Star ids, departure first and destination last. One hop is two ids. */
@@ -30,11 +45,17 @@ export interface Route {
 }
 
 /**
- * A cap on how much of the catalogue one search may walk. A search that hits it has already
- * visited more stars than any real chain passes through: the longest measured, Sol to HD 2626 at
- * 236 pc in jumps of 8 pc, settles about 7 000.
+ * A cap on how much of the catalogue one search may walk, so a hopeless question cannot run for
+ * ever. It is a budget, not a verdict: a search that spends it has proved nothing, and says so
+ * through {@link RouteSearch.gaveUp}.
+ *
+ * Sized against the catalogue actually shipped rather than against the longest route. At 20 000 a
+ * search from the Sun to HD 120147 (136 pc) in jumps of 5 pc gave up, though the chain it wanted,
+ * 50 jumps, is there to be found; a star at 170 pc needed 58. Both are found at this budget. The
+ * cost is paid by questions with no answer, which walk the whole of it: from the Sun to the
+ * farthest star at 8 pc, 0.7 s at 20 000 against 2.1 s here, in the worker.
  */
-const MAX_VISITED = 20000;
+const MAX_VISITED = 40000;
 
 /**
  * How close to the true minimum `minimumRangeBetween` works a range out: half the Routes panel's
@@ -43,6 +64,17 @@ const MAX_VISITED = 20000;
  */
 const RANGE_RESOLUTION_PC = 0.05;
 
+/**
+ * How many of `minimumRangeBetween`'s probes may give up before it answers with what it has.
+ *
+ * A probe that finds a route is quick — it heads straight for the destination — while one that
+ * gives up walks the whole search budget, about two seconds on the real catalogue. Those are also
+ * the probes that buy the least: they cannot rule anything out. Two of them is the difference
+ * between an answer of 7.96 pc in half a second and 5.76 pc in seventeen, for a star at 236 pc; it
+ * lands on 5.97 pc in five.
+ */
+const MAX_RANGE_GIVE_UPS = 2;
+
 /** A binary min-heap of star ids by priority. Duplicates are allowed; stale ones are skipped on the way out. */
 class Frontier {
   private readonly ids: number[] = [];
@@ -113,8 +145,8 @@ function rebuild(cameFrom: Map<number, number>, fromId: number, toId: number): n
 }
 
 /**
- * The shortest chain from one star to another in which no single hop exceeds `rangePc`, or
- * `null` where the catalogue holds no such chain.
+ * The shortest chain from one star to another in which no single hop exceeds `rangePc`, or no
+ * chain where the catalogue holds none within the search's budget.
  *
  * Shortest by total distance travelled rather than by number of hops: two chains of the same
  * length are not equally good, and the one that covers less ground is the one a reader means by
@@ -126,12 +158,15 @@ function rebuild(cameFrom: Map<number, number>, fromId: number, toId: number): n
  * than widening evenly in every direction. Widening evenly is what the Gaia catalogue broke. From
  * the Sun it spent its whole budget on the 20 000 stars nearest, all inside about 40 pc, and so
  * found no route to anything farther at any range; Mirfak, 155 pc out, is 27 jumps at 8 pc.
+ *
+ * "No route" and "no chain" are not the same answer: a search that spends {@link MAX_VISITED}
+ * reports that it gave up, so nothing downstream reads it as proof that no chain exists.
  */
-export function routeBetween(index: StarNeighbourhood, fromId: number, toId: number, rangePc: number): Route | null {
+export function routeBetween(index: StarNeighbourhood, fromId: number, toId: number, rangePc: number): RouteSearch {
   const origin = index.point(fromId);
   const destination = index.point(toId);
   if (fromId === toId || rangePc <= 0 || !origin || !destination) {
-    return null;
+    return { route: null, gaveUp: false };
   }
   const straightLineOn = (x: number, y: number, z: number) => Math.hypot(destination.x - x, destination.y - y, destination.z - z);
 
@@ -156,13 +191,13 @@ export function routeBetween(index: StarNeighbourhood, fromId: number, toId: num
     if (starId === toId) {
       const stars = rebuild(cameFrom, fromId, toId);
       if (stars.length === 0) {
-        return null;
+        return { route: null, gaveUp: false };
       }
       let longestHopPc = 0;
       for (let i = 1; i < stars.length; i++) {
         longestHopPc = Math.max(longestHopPc, hopTo.get(stars[i])!);
       }
-      return { stars, totalPc: costHere, longestHopPc };
+      return { route: { stars, totalPc: costHere, longestHopPc }, gaveUp: false };
     }
 
     index.forEachWithin(starId, rangePc, (neighbour, distancePc) => {
@@ -179,38 +214,51 @@ export function routeBetween(index: StarNeighbourhood, fromId: number, toId: num
     });
   }
 
-  return null;
+  // An empty frontier means the range reaches nothing further; a spent budget means only that the
+  // search stopped looking.
+  return { route: null, gaveUp: settled.size >= MAX_VISITED };
 }
 
 /**
- * The shortest range at which any chain at all exists between two stars, to within
- * `RANGE_RESOLUTION_PC`, or `null` if none does within `ceilingPc`.
+ * A range at which a chain exists between two stars — the shortest, to within
+ * `RANGE_RESOLUTION_PC`, where every shorter range could be ruled out — or `null` where no chain
+ * was found up to `ceilingPc`.
  *
- * This is what turns "no route" from a dead end into an answer: the range control can be told
- * what it would have to be raised to. The exact figure is the minimax path, the chain whose
- * longest hop is as short as possible. It used to be searched for directly, widening from the
- * departure in order of the worst hop needed, which from the Sun meant exhausting the whole dense
- * core before anything farther could be reached: it gave up with nothing after up to a minute.
- * Whether a chain exists can only become truer as the range grows, so the range is bisected
- * instead, each step one directed `routeBetween`.
+ * This is what turns "no route" from a dead end into an answer: the range control can be told what
+ * it would have to be raised to. The figure aimed at is the minimax path, the chain whose longest
+ * hop is as short as possible. It used to be searched for directly, widening from the departure in
+ * order of the worst hop needed, which from the Sun meant exhausting the whole dense core before
+ * anything farther could be reached: it gave up with nothing after up to a minute. Whether a chain
+ * exists can only become truer as the range grows, so the range is bisected instead, each step one
+ * directed `routeBetween`.
+ *
+ * Each step has to answer "is there a chain at this range", and a search that gives up answers
+ * nothing. It is still worth carrying on from — the ranges above it are the ones left to try — but
+ * the result is no longer the least range, only a range that works, and `least` says which. The
+ * number of steps is bounded for the same reason: each one that gives up walks the whole budget,
+ * and 11 s of them for a star at 236 pc bought two decimal places nobody reads.
  */
-export function minimumRangeBetween(index: StarNeighbourhood, fromId: number, toId: number, ceilingPc: number): number | null {
+export function minimumRangeBetween(index: StarNeighbourhood, fromId: number, toId: number, ceilingPc: number): RangeSearch {
   const widest = routeBetween(index, fromId, toId, ceilingPc);
-  if (!widest) {
-    return null;
+  if (!widest.route) {
+    return { rangePc: null, least: !widest.gaveUp };
   }
   let unreachable = 0;
-  let reachable = widest.longestHopPc;
-  while (reachable - unreachable > RANGE_RESOLUTION_PC) {
+  let reachable = widest.route.longestHopPc;
+  let giveUps = 0;
+  while (reachable - unreachable > RANGE_RESOLUTION_PC && giveUps < MAX_RANGE_GIVE_UPS) {
     const range = (unreachable + reachable) / 2;
-    const route = routeBetween(index, fromId, toId, range);
+    const { route, gaveUp } = routeBetween(index, fromId, toId, range);
     if (route) {
       reachable = route.longestHopPc;
     } else {
+      // A search that gave up is worth going on from — the ranges above it are the ones left to
+      // try — but it is not evidence that nothing routes here, so the answer stops being the least.
       unreachable = range;
+      giveUps += gaveUp ? 1 : 0;
     }
   }
-  return reachable;
+  return { rangePc: reachable, least: giveUps === 0 && reachable - unreachable <= RANGE_RESOLUTION_PC };
 }
 
 /** How much of a graph to keep: the links nearest a point, up to a total length. */
diff --git a/src/app/shared/astro/routing.spec.ts b/src/app/shared/astro/routing.spec.ts
index 8509a45..0cf2004 100644
--- a/src/app/shared/astro/routing.spec.ts
+++ b/src/app/shared/astro/routing.spec.ts
@@ -2,7 +2,7 @@ import { describe, expect, it } from 'vitest';
 
 import { jumpLinkSegments, minimumRangeBetween, routeBetween } from './jump-links';
 import { answerRouting, indexCatalogue } from './routing';
-import { StarNeighbourhood } from './star-neighbourhood';
+import { StarNeighbourhood, StarPoint } from './star-neighbourhood';
 
 /** Stars a parsec apart along x, then a gap of 5 pc to one more. */
 const POINTS = [...Array.from({ length: 5 }, (_, i) => ({ id: 10 + i, x: i, y: 0, z: 0 })), { id: 99, x: 9, y: 0, z: 0 }];
@@ -25,6 +25,16 @@ describe('indexCatalogue', () => {
   });
 });
 
+/** The same index, counting the neighbour queries a search makes through it. */
+class CountingNeighbourhood extends StarNeighbourhood {
+  queries = 0;
+
+  override forEachWithin(id: number, radiusPc: number, visit: (neighbour: StarPoint, distancePc: number) => void): void {
+    this.queries++;
+    super.forEachWithin(id, radiusPc, visit);
+  }
+}
+
 describe('answerRouting', () => {
   const index = indexCatalogue(catalogue());
   const direct = new StarNeighbourhood(POINTS);
@@ -32,16 +42,43 @@ describe('answerRouting', () => {
   it('answers a route the range allows, with nothing to raise it to', () => {
     const answer = answerRouting(index, { kind: 'route', requestId: 7, fromId: 10, toId: 14, rangePc: 1.5, ceilingPc: 8 });
 
-    expect(answer).toEqual({ kind: 'route', requestId: 7, route: routeBetween(direct, 10, 14, 1.5), neededRangePc: null });
+    expect(answer).toEqual({ kind: 'route', requestId: 7, route: routeBetween(direct, 10, 14, 1.5).route, neededRangePc: null, gaveUp: false });
   });
 
   it('answers a route the range does not allow with the range that would', () => {
     const answer = answerRouting(index, { kind: 'route', requestId: 8, fromId: 10, toId: 99, rangePc: 1.5, ceilingPc: 8 });
 
-    expect(answer).toEqual({ kind: 'route', requestId: 8, route: null, neededRangePc: minimumRangeBetween(direct, 10, 99, 8) });
+    expect(answer).toEqual({ kind: 'route', requestId: 8, route: null, neededRangePc: minimumRangeBetween(direct, 10, 99, 8).rangePc, gaveUp: false });
     expect(answer.kind === 'route' && answer.neededRangePc).toBeCloseTo(5, 1);
   });
 
+  it('passes on that the search gave up, rather than reporting no route', () => {
+    // A crowd larger than a search's budget around the departure, and a destination nothing reaches:
+    // the answer is "it gave up", and the scene has to be able to tell that from "there is none".
+    let seed = 5;
+    const random = () => ((seed = (seed * 1103515245 + 12345) % 2147483648) / 2147483648) * 10 - 5;
+    const crowd: StarPoint[] = Array.from({ length: 45000 }, (_, i) => ({ id: 1000 + i, x: random(), y: random(), z: random() }));
+    const knot = new StarNeighbourhood([{ id: 0, x: 0, y: 0, z: 0 }, ...crowd, { id: 99, x: 500, y: 0, z: 0 }], 0.5);
+
+    const answer = answerRouting(knot, { kind: 'route', requestId: 12, fromId: 0, toId: 99, rangePc: 0.5, ceilingPc: 0.5 });
+
+    expect(answer).toMatchObject({ route: null, neededRangePc: null, gaveUp: true });
+  });
+
+  it('asks the ceiling its question once, rather than searching it again to answer it', () => {
+    // At the panel's widest range the refused route and the range search are the same question, run
+    // with the same arguments over the same index: the second pays the whole budget for the answer
+    // the first already gave.
+    const counting = new CountingNeighbourhood(POINTS);
+    const oneSearch = new CountingNeighbourhood(POINTS);
+    routeBetween(oneSearch, 10, 99, 3);
+
+    const answer = answerRouting(counting, { kind: 'route', requestId: 11, fromId: 10, toId: 99, rangePc: 3, ceilingPc: 3 });
+
+    expect(answer).toMatchObject({ route: null, neededRangePc: null });
+    expect(counting.queries).toBe(oneSearch.queries);
+  });
+
   it('offers nothing to raise to when even the ceiling does not reach', () => {
     const answer = answerRouting(index, { kind: 'route', requestId: 9, fromId: 10, toId: 99, rangePc: 1.5, ceilingPc: 3 });
 
diff --git a/src/app/shared/astro/routing.ts b/src/app/shared/astro/routing.ts
index f917d7c..6c10473 100644
--- a/src/app/shared/astro/routing.ts
+++ b/src/app/shared/astro/routing.ts
@@ -26,7 +26,11 @@ export type RoutingRequest =
   | { readonly kind: 'links'; readonly requestId: number; readonly rangePc: number; readonly drawn: Uint32Array; readonly budget?: LinkBudget };
 
 export type RoutingResponse =
-  | { readonly kind: 'route'; readonly requestId: number; readonly route: Route | null; readonly neededRangePc: number | null }
+  /**
+   * `gaveUp` is true when the searches spent their budget rather than looking everywhere: there
+   * being no route and no range to offer is then what was found, not what exists.
+   */
+  | { readonly kind: 'route'; readonly requestId: number; readonly route: Route | null; readonly neededRangePc: number | null; readonly gaveUp: boolean }
   | { readonly kind: 'links'; readonly requestId: number; readonly segments: Float32Array }
   /** The question threw in the worker. Sent back so the request settles instead of waiting for good. */
   | { readonly kind: 'failed'; readonly requestId: number; readonly message: string };
@@ -37,8 +41,9 @@ export function indexCatalogue({ ids, positions }: RoutingCatalogue): StarNeighb
 }
 
 /**
- * Answers one request. A route that cannot be made comes back with the range that would make
- * one, searched no wider than `ceilingPc`, so a refusal is always also an offer.
+ * Answers one request. A route that cannot be made comes back with the range that would make one,
+ * searched no wider than `ceilingPc`, so a refusal is usually also an offer — unless the searches
+ * gave up, which is reported rather than passed off as "there is no route".
  */
 export function answerRouting(index: StarNeighbourhood, request: RoutingRequest): RoutingResponse {
   if (request.kind === 'links') {
@@ -47,11 +52,12 @@ export function answerRouting(index: StarNeighbourhood, request: RoutingRequest)
     const drawn = new StarNeighbourhood(Array.from(request.drawn, (at) => index.pointAt(at)), request.rangePc);
     return { kind: 'links', requestId: request.requestId, segments: jumpLinkSegments(drawn, request.rangePc, request.budget) };
   }
-  const route = routeBetween(index, request.fromId, request.toId, request.rangePc);
-  return {
-    kind: 'route',
-    requestId: request.requestId,
-    route,
-    neededRangePc: route ? null : minimumRangeBetween(index, request.fromId, request.toId, request.ceilingPc)
-  };
+  const { route, gaveUp } = routeBetween(index, request.fromId, request.toId, request.rangePc);
+  // At the ceiling the question has just been asked: the range search would repeat it, identically
+  // and at the same cost, before bisecting below it.
+  if (route || request.rangePc >= request.ceilingPc) {
+    return { kind: 'route', requestId: request.requestId, route, neededRangePc: null, gaveUp: !route && gaveUp };
+  }
+  const needed = minimumRangeBetween(index, request.fromId, request.toId, request.ceilingPc);
+  return { kind: 'route', requestId: request.requestId, route: null, neededRangePc: needed.rangePc, gaveUp: gaveUp || !needed.least };
 }