diff --git a/e2e/__tests__/__snapshots__/nativeEsm.test.ts.snap b/e2e/__tests__/__snapshots__/nativeEsm.test.ts.snap
index e530b3607f71..b5a531aca80d 100644
--- a/e2e/__tests__/__snapshots__/nativeEsm.test.ts.snap
+++ b/e2e/__tests__/__snapshots__/nativeEsm.test.ts.snap
@@ -1,17 +1,17 @@
 // Jest Snapshot v1, https://goo.gl/fbAQLP
 
-exports[`on node >=14.3.0 supports top-level await 1`] = `
+exports[`on node >=12.16.0 runs test with native ESM 1`] = `
 Test Suites: 1 passed, 1 total
-Tests:       1 passed, 1 total
+Tests:       21 passed, 21 total
 Snapshots:   0 total
 Time:        <<REPLACED>>
-Ran all test suites matching /native-esm.tla.test.js/i.
+Ran all test suites matching /native-esm.test.js/i.
 `;
 
-exports[`on node ^12.16.0 || >=13.7.0 runs test with native ESM 1`] = `
+exports[`on node >=14.3.0 supports top-level await 1`] = `
 Test Suites: 1 passed, 1 total
-Tests:       21 passed, 21 total
+Tests:       1 passed, 1 total
 Snapshots:   0 total
 Time:        <<REPLACED>>
-Ran all test suites matching /native-esm.test.js/i.
+Ran all test suites matching /native-esm.tla.test.js/i.
 `;
diff --git a/e2e/__tests__/customEsmTestSequencers.test.ts b/e2e/__tests__/customEsmTestSequencers.test.ts
index 6fdadb280af8..706df262b620 100644
--- a/e2e/__tests__/customEsmTestSequencers.test.ts
+++ b/e2e/__tests__/customEsmTestSequencers.test.ts
@@ -11,7 +11,7 @@ import {extractSummary} from '../Utils';
 import runJest from '../runJest';
 const dir = path.resolve(__dirname, '../custom-esm-test-sequencer');
 
-onNodeVersions('^12.16.0 || >=13.7.0', () => {
+onNodeVersions('>=12.16.0', () => {
   test('run prioritySequence', () => {
     const result = runJest(dir, ['-i'], {
       nodeOptions: '--experimental-vm-modules --no-warnings',
diff --git a/e2e/__tests__/customReporters.test.ts b/e2e/__tests__/customReporters.test.ts
index e2210710c50b..e5a5cf3508aa 100644
--- a/e2e/__tests__/customReporters.test.ts
+++ b/e2e/__tests__/customReporters.test.ts
@@ -161,7 +161,7 @@ describe('Custom Reporters Integration', () => {
     expect(exitCode).toBe(1);
   });
 
-  onNodeVersions('^12.17.0 || >=13.2.0', () => {
+  onNodeVersions('>=12.17.0', () => {
     test('supports reporter written in ESM', () => {
       writeFiles(DIR, {
         '__tests__/test.test.js': `test('test', () => {});`,
diff --git a/e2e/__tests__/detectOpenHandles.ts b/e2e/__tests__/detectOpenHandles.ts
index cd6cdfa17225..3c632f03cd0c 100644
--- a/e2e/__tests__/detectOpenHandles.ts
+++ b/e2e/__tests__/detectOpenHandles.ts
@@ -82,7 +82,7 @@ it('does not report crypto random data', () => {
   expect(textAfterTest).toBe('');
 });
 
-onNodeVersions('>=11.10.0', () => {
+onNodeVersions('>=12', () => {
   it('does not report ELD histograms', () => {
     const {stderr} = runJest('detect-open-handles', [
       'histogram',
@@ -110,7 +110,7 @@ describe('notify', () => {
   });
 });
 
-onNodeVersions('>=11', () => {
+onNodeVersions('>=12', () => {
   it('does not report timeouts using unref', () => {
     // The test here is basically that it exits cleanly without reporting anything (does not need `until`)
     const {stderr} = runJest('detect-open-handles', [
diff --git a/e2e/__tests__/esmConfigFile.test.ts b/e2e/__tests__/esmConfigFile.test.ts
index 14dc9d715400..fa4092ad7428 100644
--- a/e2e/__tests__/esmConfigFile.test.ts
+++ b/e2e/__tests__/esmConfigFile.test.ts
@@ -20,7 +20,7 @@ test('reads config from cjs file', () => {
   });
 });
 
-onNodeVersions('^12.17.0 || >=13.2.0', () => {
+onNodeVersions('>=12.17.0', () => {
   test('reads config from mjs file', () => {
     const {configs} = getConfig('esm-config/mjs', [], {
       skipPkgJsonCheck: true,
diff --git a/e2e/__tests__/globalSetup.test.ts b/e2e/__tests__/globalSetup.test.ts
index 900c28345d19..21763b38d3e6 100644
--- a/e2e/__tests__/globalSetup.test.ts
+++ b/e2e/__tests__/globalSetup.test.ts
@@ -197,7 +197,7 @@ test('properly handle rejections', () => {
   expect(stderr).toContain('reason: undefined');
 });
 
-onNodeVersions('^12.17.0 || >=13.2.0', () => {
+onNodeVersions('>=12.17.0', () => {
   test('globalSetup works with ESM modules', () => {
     const {exitCode} = runJest('global-setup-esm', [`--no-cache`], {
       nodeOptions: '--experimental-vm-modules --no-warnings',
diff --git a/e2e/__tests__/globalTeardown.test.ts b/e2e/__tests__/globalTeardown.test.ts
index 3ac81a0e49e3..aa60338bfd60 100644
--- a/e2e/__tests__/globalTeardown.test.ts
+++ b/e2e/__tests__/globalTeardown.test.ts
@@ -136,7 +136,7 @@ test('globalTeardown throws with named export', () => {
   );
 });
 
-onNodeVersions('^12.17.0 || >=13.2.0', () => {
+onNodeVersions('>=12.17.0', () => {
   test('globalTeardown works with ESM modules', () => {
     const {exitCode} = runJest('global-teardown-esm', [`--no-cache`], {
       nodeOptions: '--experimental-vm-modules --no-warnings',
diff --git a/e2e/__tests__/nativeAsyncMock.test.ts b/e2e/__tests__/nativeAsyncMock.test.ts
index e0e43cb1d02e..f37305a4390c 100644
--- a/e2e/__tests__/nativeAsyncMock.test.ts
+++ b/e2e/__tests__/nativeAsyncMock.test.ts
@@ -12,10 +12,6 @@ import runJest from '../runJest';
 const dir = path.resolve(__dirname, '..', 'native-async-mock');
 
 test('mocks async functions', () => {
-  if (process.versions.node < '7.6.0') {
-    return;
-  }
-
   runYarnInstall(dir);
 
   // --no-cache because babel can cache stuff and result in false green
diff --git a/e2e/__tests__/nativeEsm.test.ts b/e2e/__tests__/nativeEsm.test.ts
index 1a3a7adb63ce..8aa81dbf1b69 100644
--- a/e2e/__tests__/nativeEsm.test.ts
+++ b/e2e/__tests__/nativeEsm.test.ts
@@ -21,7 +21,7 @@ test('test config is without transform', () => {
 });
 
 // The versions where vm.Module exists and commonjs with "exports" is not broken
-onNodeVersions('^12.16.0 || >=13.7.0', () => {
+onNodeVersions('>=12.16.0', () => {
   test('runs test with native ESM', () => {
     const {exitCode, stderr, stdout} = runJest(DIR, ['native-esm.test.js'], {
       nodeOptions: '--experimental-vm-modules --no-warnings',
diff --git a/e2e/__tests__/nativeEsmTypescript.test.ts b/e2e/__tests__/nativeEsmTypescript.test.ts
index d8ed0b7d59e4..ad1d817f8a16 100644
--- a/e2e/__tests__/nativeEsmTypescript.test.ts
+++ b/e2e/__tests__/nativeEsmTypescript.test.ts
@@ -12,7 +12,7 @@ import {json as runJest} from '../runJest';
 const DIR = resolve(__dirname, '../native-esm-typescript');
 
 // The versions where vm.Module exists and commonjs with "exports" is not broken
-onNodeVersions('^12.16.0 || >=13.7.0', () => {
+onNodeVersions('>=12.16.0', () => {
   test('runs TS test with native ESM', () => {
     const {exitCode, json} = runJest(DIR, [], {
       nodeOptions: '--experimental-vm-modules --no-warnings',
diff --git a/e2e/__tests__/presets.test.ts b/e2e/__tests__/presets.test.ts
index d7d24979619c..2a8edc665a49 100644
--- a/e2e/__tests__/presets.test.ts
+++ b/e2e/__tests__/presets.test.ts
@@ -19,7 +19,7 @@ test.each(['js', 'cjs'])('supports %s preset', presetDir => {
   expect(result.exitCode).toBe(0);
 });
 
-onNodeVersions('^12.17.0 || >=13.2.0', () => {
+onNodeVersions('>=12.17.0', () => {
   // eslint-disable-next-line jest/no-identical-title
   test.each(['mjs', 'js-type-module'])('supports %s preset', presetDir => {
     const result = runJest(`presets/${presetDir}`);
diff --git a/e2e/__tests__/resolveConditions.test.ts b/e2e/__tests__/resolveConditions.test.ts
index db9336320675..ee7c00f6f12d 100644
--- a/e2e/__tests__/resolveConditions.test.ts
+++ b/e2e/__tests__/resolveConditions.test.ts
@@ -17,7 +17,7 @@ beforeAll(() => {
 });
 
 // The versions where vm.Module exists and commonjs with "exports" is not broken
-onNodeVersions('^12.16.0 || >=13.7.0', () => {
+onNodeVersions('>=12.16.0', () => {
   test('resolves package exports correctly with custom resolver', () => {
     // run multiple times to ensure there are no caching errors
     for (let i = 0; i < 5; i++) {
diff --git a/e2e/__tests__/testEnvironmentEsm.ts b/e2e/__tests__/testEnvironmentEsm.ts
index 1b604d3f9273..cb41ad429934 100644
--- a/e2e/__tests__/testEnvironmentEsm.ts
+++ b/e2e/__tests__/testEnvironmentEsm.ts
@@ -10,7 +10,7 @@ import {onNodeVersions} from '@jest/test-utils';
 import runJest from '../runJest';
 
 // The versions where vm.Module exists and commonjs with "exports" is not broken
-onNodeVersions('^12.16.0 || >=13.7.0', () => {
+onNodeVersions('>=12.16.0', () => {
   it('support test environment written in ESM', () => {
     const DIR = resolve(__dirname, '../test-environment-esm');
     const {exitCode} = runJest(DIR);
diff --git a/e2e/__tests__/transform.test.ts b/e2e/__tests__/transform.test.ts
index 72bd1a4510df..5e088066e7d7 100644
--- a/e2e/__tests__/transform.test.ts
+++ b/e2e/__tests__/transform.test.ts
@@ -277,7 +277,7 @@ describe('transform-testrunner', () => {
   });
 });
 
-onNodeVersions('^12.17.0 || >=13.2.0', () => {
+onNodeVersions('>=12.17.0', () => {
   describe('esm-transformer', () => {
     const dir = path.resolve(__dirname, '../transform/esm-transformer');
 
diff --git a/e2e/__tests__/watch-plugins.test.ts b/e2e/__tests__/watch-plugins.test.ts
index 59eff8a77eea..4137e03854bf 100644
--- a/e2e/__tests__/watch-plugins.test.ts
+++ b/e2e/__tests__/watch-plugins.test.ts
@@ -26,7 +26,7 @@ test.each(['js', 'cjs'])('supports %s watch plugins', async watchPluginDir => {
   await testRun.end();
 });
 
-onNodeVersions('^12.17.0 || >=13.2.0', () => {
+onNodeVersions('>=12.17.0', () => {
   test.each(['mjs', 'js-type-module'])(
     // eslint-disable-next-line jest/no-identical-title
     'supports %s watch plugins',
diff --git a/packages/expect/src/__tests__/matchers-toStrictEqual.property.test.ts b/packages/expect/src/__tests__/matchers-toStrictEqual.property.test.ts
index 185a814d0b9b..1f9d293e162f 100644
--- a/packages/expect/src/__tests__/matchers-toStrictEqual.property.test.ts
+++ b/packages/expect/src/__tests__/matchers-toStrictEqual.property.test.ts
@@ -8,7 +8,6 @@
 
 import assert from 'assert';
 import fc from 'fast-check';
-import {onNodeVersions} from '@jest/test-utils';
 import expect from '..';
 import {
   anythingSettings,
@@ -58,20 +57,18 @@ describe('toStrictEqual', () => {
     );
   });
 
-  onNodeVersions('>=9', () => {
-    it('should be equivalent to Node deepStrictEqual', () => {
-      fc.assert(
-        fc.property(
-          fc.anything(anythingSettings),
-          fc.anything(anythingSettings),
-          (a, b) => {
-            expect(safeExpectStrictEqual(a, b)).toBe(
-              safeAssertDeepStrictEqual(a, b),
-            );
-          },
-        ),
-        assertSettings,
-      );
-    });
+  it('should be equivalent to Node deepStrictEqual', () => {
+    fc.assert(
+      fc.property(
+        fc.anything(anythingSettings),
+        fc.anything(anythingSettings),
+        (a, b) => {
+          expect(safeExpectStrictEqual(a, b)).toBe(
+            safeAssertDeepStrictEqual(a, b),
+          );
+        },
+      ),
+      assertSettings,
+    );
   });
 });