diff --git a/e2e/two-planes.spec.ts b/e2e/two-planes.spec.ts
index 6e8d557..490e3ec 100644
--- a/e2e/two-planes.spec.ts
+++ b/e2e/two-planes.spec.ts
@@ -226,7 +226,13 @@ async function healPlaneHome(page: Page, planeId: string): Promise<void> {
   if (p.locationIcao !== HUB) {
     // ISS-057: the landing above slowed the sim to 1× — setScale restores 1000× for the return leg.
     await setScale(page, SCALE);
-    expect((await page.request.post(`/api/planes/${planeId}/fly`, { data: { destIcao: HUB } })).status()).toBe(200);
+    let flyHome = await page.request.post(`/api/planes/${planeId}/fly`, { data: { destIcao: HUB } });
+    if (flyHome.status() === 409) {
+      // A long outbound leg can leave the tank too empty for the return — top up and retry.
+      expect((await page.request.post(`/api/planes/${planeId}/refuel`)).status()).toBe(200);
+      flyHome = await page.request.post(`/api/planes/${planeId}/fly`, { data: { destIcao: HUB } });
+    }
+    expect(flyHome.status()).toBe(200);
     await expect
       .poll(async () => ((await getState(page)).planes.find((x) => x.id === planeId)?.locationIcao ?? ''), {
         timeout: 240_000,
@@ -374,6 +380,9 @@ test('two planes fly in parallel; the last landing slows to 1× and the next dis
   expect(landed.packages.find((p) => p.id === pkgA.id)?.status).toBe('delivered');
   expect(landed.packages.find((p) => p.id === pkgB.id)?.status).toBe('delivered');
 
+  // The outbound to the range edge left the tank nearly empty — top up for the return leg.
+  expect((await page.request.post(`/api/planes/${secondId}/refuel`)).status()).toBe(200);
+
   // Resume semantics: with the starter still grounded, dispatching the second plane does NOT resume…
   const flyB2 = await page.request.post(`/api/planes/${secondId}/fly`, { data: { destIcao: HUB } });
   expect(flyB2.status()).toBe(200);