diff --git a/src/utils/__tests__/async-test.js b/src/utils/__tests__/async-test.js
index a36f815d011..dc67e76bd92 100644
--- a/src/utils/__tests__/async-test.js
+++ b/src/utils/__tests__/async-test.js
@@ -1,7 +1,55 @@
 /* @flow strict-local */
-import { sleep } from '../async';
+import { sleep, BackoffMachine } from '../async';
 import { assertUsingModernFakeTimers } from '../../__tests__/lib/fakeTimers';
 
+describe('BackoffMachine', () => {
+  beforeAll(() => {
+    assertUsingModernFakeTimers();
+  });
+
+  afterEach(() => {
+    expect(jest.getTimerCount()).toBe(0);
+    jest.clearAllTimers();
+  });
+
+  const measureWait = async (promise: Promise<void>) => {
+    const start = Date.now();
+    jest.runOnlyPendingTimers();
+    await promise;
+    return Date.now() - start;
+  };
+
+  test('timeouts are random from zero to 100ms, 200ms, 400ms, 800ms...', async () => {
+    // This is a randomized test. NUM_TRIALS is chosen so that the failure
+    // probability < 1e-9. There are 2 * 11 assertions, and each one has a
+    // failure probability < 1e-12; see below.
+    const NUM_TRIALS = 100;
+    const expectedMaxDurations = [100, 200, 400, 800, 1600, 3200, 6400, 10000, 10000, 10000, 10000];
+
+    const trialResults: Array<number[]> = [];
+
+    for (let i = 0; i < NUM_TRIALS; i++) {
+      const resultsForThisTrial = [];
+      const backoffMachine = new BackoffMachine();
+      for (let j = 0; j < expectedMaxDurations.length; j++) {
+        const duration = await measureWait(backoffMachine.wait());
+        resultsForThisTrial.push(duration);
+      }
+      trialResults.push(resultsForThisTrial);
+    }
+
+    expectedMaxDurations.forEach((expectedMax, i) => {
+      const maxFromAllTrials = Math.max(...trialResults.map(r => r[i]));
+      const minFromAllTrials = Math.min(...trialResults.map(r => r[i]));
+
+      // Each of these assertions has a failure probability of:
+      //     0.75 ** NUM_TRIALS = 0.75 ** 100 < 1e-12
+      expect(minFromAllTrials).toBeLessThan(expectedMax * 0.25);
+      expect(maxFromAllTrials).toBeGreaterThan(expectedMax * 0.75);
+    });
+  });
+});
+
 const sleepMeasure = async (expectedMs: number) => {
   const start = Date.now();
   await sleep(expectedMs);
diff --git a/src/utils/__tests__/backoffMachine-test.js b/src/utils/__tests__/backoffMachine-test.js
deleted file mode 100644
index 40548e80f07..00000000000
--- a/src/utils/__tests__/backoffMachine-test.js
+++ /dev/null
@@ -1,54 +0,0 @@
-/* @flow strict-local */
-import { BackoffMachine } from '../async';
-
-// Since BackoffMachine is in async.js, these tests *should* be in
-// async-test.js. But doing that introduces some interference between these
-// tests and the other Lolex-based tests, since Jest is running both of them in
-// the same environment in parallel. This may be resolved out of the box in Jest
-// 26, and it might even be safe in Jest 25.1.0 with a custom environment
-// (https://github.com/facebook/jest/pull/8897). But as of 2020-03, putting them
-// in a separate file is our workaround.
-
-describe('BackoffMachine', () => {
-  afterEach(() => {
-    expect(jest.getTimerCount()).toBe(0);
-    jest.clearAllTimers();
-  });
-
-  const measureWait = async (promise: Promise<void>) => {
-    const start = Date.now();
-    jest.runOnlyPendingTimers();
-    await promise;
-    return Date.now() - start;
-  };
-
-  test('timeouts are random from zero to 100ms, 200ms, 400ms, 800ms...', async () => {
-    // This is a randomized test. NUM_TRIALS is chosen so that the failure
-    // probability < 1e-9. There are 2 * 11 assertions, and each one has a
-    // failure probability < 1e-12; see below.
-    const NUM_TRIALS = 100;
-    const expectedMaxDurations = [100, 200, 400, 800, 1600, 3200, 6400, 10000, 10000, 10000, 10000];
-
-    const trialResults: Array<number[]> = [];
-
-    for (let i = 0; i < NUM_TRIALS; i++) {
-      const resultsForThisTrial = [];
-      const backoffMachine = new BackoffMachine();
-      for (let j = 0; j < expectedMaxDurations.length; j++) {
-        const duration = await measureWait(backoffMachine.wait());
-        resultsForThisTrial.push(duration);
-      }
-      trialResults.push(resultsForThisTrial);
-    }
-
-    expectedMaxDurations.forEach((expectedMax, i) => {
-      const maxFromAllTrials = Math.max(...trialResults.map(r => r[i]));
-      const minFromAllTrials = Math.min(...trialResults.map(r => r[i]));
-
-      // Each of these assertions has a failure probability of:
-      //     0.75 ** NUM_TRIALS = 0.75 ** 100 < 1e-12
-      expect(minFromAllTrials).toBeLessThan(expectedMax * 0.25);
-      expect(maxFromAllTrials).toBeGreaterThan(expectedMax * 0.75);
-    });
-  });
-});