diff --git a/test/remote-wake.test.ts b/test/remote-wake.test.ts
index f1fe7f06..22b96db6 100644
--- a/test/remote-wake.test.ts
+++ b/test/remote-wake.test.ts
@@ -559,9 +559,14 @@ describe('RemoteWakeRegistry', () => {
       h.registry.ensureAwake(h.session, { force: true, timeoutMs: REMOTE_WAKE_REQUEST_READY_TIMEOUT_MS })
     ).resolves.toBe(true);
     expect(h.waitUntilReady).toHaveBeenCalledWith(remote, {
-      timeoutMs: REMOTE_WAKE_REQUEST_READY_TIMEOUT_MS,
+      timeoutMs: expect.any(Number),
       signal: expect.any(AbortSignal),
     });
+    // Not asserted to the millisecond: the wake's own elapsed time is subtracted, so a
+    // slow runner lands a few ms under the budget.
+    const [, readyOpts] = h.waitUntilReady.mock.calls[0] as [unknown, { timeoutMs: number; signal: AbortSignal }];
+    expect(readyOpts.timeoutMs).toBeLessThanOrEqual(REMOTE_WAKE_REQUEST_READY_TIMEOUT_MS);
+    expect(readyOpts.timeoutMs).toBeGreaterThan(REMOTE_WAKE_REQUEST_READY_TIMEOUT_MS - 1_000);
   });
 });
 
diff --git a/test/routes/session-routes.test.ts b/test/routes/session-routes.test.ts
index 11b1e755..466ab738 100644
--- a/test/routes/session-routes.test.ts
+++ b/test/routes/session-routes.test.ts
@@ -2182,10 +2182,15 @@ describe('session-routes', () => {
           // The request budget, not the 90 s session default: the reverse proxy would
           // cut the request at 60 s while the session was still being built.
           expect(wakeWaitUntilReady).toHaveBeenCalledWith(expect.objectContaining({ hostId: 'hufflepuff' }), {
-            timeoutMs: REMOTE_WAKE_REQUEST_READY_TIMEOUT_MS,
+            timeoutMs: expect.any(Number),
             // The shutdown signal rides along so `WebServer.stop()` can end the poll.
             signal: expect.any(AbortSignal),
           });
+          // Not asserted to the millisecond: the wake's own elapsed time is subtracted,
+          // so a slow runner lands a few ms under the budget.
+          const [, readyOpts] = wakeWaitUntilReady.mock.calls[0] as unknown as [unknown, { timeoutMs: number }];
+          expect(readyOpts.timeoutMs).toBeLessThanOrEqual(REMOTE_WAKE_REQUEST_READY_TIMEOUT_MS);
+          expect(readyOpts.timeoutMs).toBeGreaterThan(REMOTE_WAKE_REQUEST_READY_TIMEOUT_MS - 1_000);
         } finally {
           startShell.mockRestore();
         }