diff --git a/tests/src/rules/first.js b/tests/src/rules/first.js
index 9d27870677..05328e51e9 100644
--- a/tests/src/rules/first.js
+++ b/tests/src/rules/first.js
@@ -80,7 +80,6 @@ ruleTester.run('first', rule, {
 
 context('TypeScript', function () {
   getTSParsers()
-    .filter((parser) => parser !== require.resolve('typescript-eslint-parser'))
     .forEach((parser) => {
       const parserConfig = {
         parser,
diff --git a/tests/src/rules/max-dependencies.js b/tests/src/rules/max-dependencies.js
index bab38496e0..6d80bbf046 100644
--- a/tests/src/rules/max-dependencies.js
+++ b/tests/src/rules/max-dependencies.js
@@ -1,8 +1,6 @@
 import { test, getTSParsers } from '../utils';
 
 import { RuleTester } from 'eslint';
-import eslintPkg from 'eslint/package.json';
-import semver from 'semver';
 
 const ruleTester = new RuleTester();
 const rule = require('rules/max-dependencies');
@@ -91,43 +89,46 @@ ruleTester.run('max-dependencies', rule, {
   ],
 });
 
-(semver.satisfies(eslintPkg.version, '>5.0.0') ? describe.skip : describe)('TypeScript', () => {
-  getTSParsers().forEach((parser) => {
-    ruleTester.run(`max-dependencies (${parser.replace(process.cwd(), '.')})`, rule, {
-      valid: [    
-        test({
-          code: 'import type { x } from \'./foo\'; import { y } from \'./bar\';',
-          parser,
-          options: [{
-            max: 1,
-            ignoreTypeImports: true,
-          }],
-        }),
-      ],
-      invalid: [    
-        test({
-          code: 'import type { x } from \'./foo\'; import type { y } from \'./bar\'',
-          parser,
-          options: [{
-            max: 1,
-          }],
-          errors: [
-            'Maximum number of dependencies (1) exceeded.',
-          ],
-        }),
-    
-        test({
-          code: 'import type { x } from \'./foo\'; import type { y } from \'./bar\'; import type { z } from \'./baz\'',
-          parser,
-          options: [{
-            max: 2,
-            ignoreTypeImports: false,
-          }],
-          errors: [
-            'Maximum number of dependencies (2) exceeded.',
-          ],
-        }),
-      ],
+describe('TypeScript', () => {
+  getTSParsers()
+    // Type-only imports were added in TypeScript ESTree 2.23.0
+    .filter((parser) => parser !== require.resolve('typescript-eslint-parser'))
+    .forEach((parser) => {
+      ruleTester.run(`max-dependencies (${parser.replace(process.cwd(), '.')})`, rule, {
+        valid: [
+          test({
+            code: 'import type { x } from \'./foo\'; import { y } from \'./bar\';',
+            parser,
+            options: [{
+              max: 1,
+              ignoreTypeImports: true,
+            }],
+          }),
+        ],
+        invalid: [
+          test({
+            code: 'import type { x } from \'./foo\'; import type { y } from \'./bar\'',
+            parser,
+            options: [{
+              max: 1,
+            }],
+            errors: [
+              'Maximum number of dependencies (1) exceeded.',
+            ],
+          }),
+
+          test({
+            code: 'import type { x } from \'./foo\'; import type { y } from \'./bar\'; import type { z } from \'./baz\'',
+            parser,
+            options: [{
+              max: 2,
+              ignoreTypeImports: false,
+            }],
+            errors: [
+              'Maximum number of dependencies (2) exceeded.',
+            ],
+          }),
+        ],
+      });
     });
-  });
 });
diff --git a/tests/src/rules/no-duplicates.js b/tests/src/rules/no-duplicates.js
index e550b63ce7..ad39543f81 100644
--- a/tests/src/rules/no-duplicates.js
+++ b/tests/src/rules/no-duplicates.js
@@ -417,6 +417,7 @@ import {x,y} from './foo'
 
 context('TypeScript', function () {
   getNonDefaultParsers()
+    // Type-only imports were added in TypeScript ESTree 2.23.0
     .filter((parser) => parser !== require.resolve('typescript-eslint-parser'))
     .forEach((parser) => {
       const parserConfig = {
diff --git a/tests/src/rules/no-extraneous-dependencies.js b/tests/src/rules/no-extraneous-dependencies.js
index 29604af170..852dbdf4e7 100644
--- a/tests/src/rules/no-extraneous-dependencies.js
+++ b/tests/src/rules/no-extraneous-dependencies.js
@@ -2,8 +2,6 @@ import { getTSParsers, test, testFilePath } from '../utils';
 import typescriptConfig from '../../../config/typescript';
 import path from 'path';
 import fs from 'fs';
-import semver from 'semver';
-import eslintPkg from 'eslint/package.json';
 
 import { RuleTester } from 'eslint';
 import flatMap from 'array.prototype.flatmap';
@@ -380,18 +378,19 @@ ruleTester.run('no-extraneous-dependencies', rule, {
   ],
 });
 
-// TODO: figure out why these tests fail in eslint 4
-(semver.satisfies(eslintPkg.version, '^4') ? describe.skip : describe)('TypeScript', () => {
-  getTSParsers().forEach((parser) => {
-    const parserConfig = {
-      parser,
-      settings: {
-        'import/parsers': { [parser]: ['.ts'] },
-        'import/resolver': { 'eslint-import-resolver-typescript': true },
-      },
-    };
+describe('TypeScript', () => {
+  getTSParsers()
+    // Type-only imports were added in TypeScript ESTree 2.23.0
+    .filter((parser) => parser !== require.resolve('typescript-eslint-parser'))
+    .forEach((parser) => {
+      const parserConfig = {
+        parser,
+        settings: {
+          'import/parsers': { [parser]: ['.ts'] },
+          'import/resolver': { 'eslint-import-resolver-typescript': true },
+        },
+      };
 
-    if (parser !== require.resolve('typescript-eslint-parser')) {
       ruleTester.run('no-extraneous-dependencies', rule, {
         valid: [
           test(Object.assign({
@@ -409,45 +408,22 @@ ruleTester.run('no-extraneous-dependencies', rule, {
           }, parserConfig)),
         ],
       });
-    } else {
-      ruleTester.run('no-extraneous-dependencies', rule, {
-        valid: [],
-        invalid: [
-          test(Object.assign({
-            code: 'import T from "a"; /* typescript-eslint-parser */',
-            options: [{ packageDir: packageDirWithTypescriptDevDependencies, devDependencies: false }],
-            errors: [{
-              message: "'a' should be listed in the project's dependencies, not devDependencies.",
-            }],
-          }, parserConfig)),
-          test(Object.assign({
-            code: 'import type T from "a"; /* typescript-eslint-parser */',
-            options: [{ packageDir: packageDirWithTypescriptDevDependencies, devDependencies: false }],
-            errors: [{
-              message: "'a' should be listed in the project's dependencies, not devDependencies.",
-            }],
-          }, parserConfig)),
-        ],
-      });
-    }
-  });
+    });
 });
 
-if (semver.satisfies(eslintPkg.version, '>5.0.0')) {
-  typescriptRuleTester.run('no-extraneous-dependencies typescript type imports', rule, {
-    valid: [
-      test({
-        code: 'import type MyType from "not-a-dependency";',
-        filename: testFilePath('./no-unused-modules/typescript/file-ts-a.ts'),
-        parser: require.resolve('babel-eslint'),
-      }),
-      test({
-        code: 'import type { MyType } from "not-a-dependency";',
-        filename: testFilePath('./no-unused-modules/typescript/file-ts-a.ts'),
-        parser: require.resolve('babel-eslint'),
-      }),
-    ],
-    invalid: [
-    ],
-  });
-}
+typescriptRuleTester.run('no-extraneous-dependencies typescript type imports', rule, {
+  valid: [
+    test({
+      code: 'import type MyType from "not-a-dependency";',
+      filename: testFilePath('./no-unused-modules/typescript/file-ts-a.ts'),
+      parser: require.resolve('babel-eslint'),
+    }),
+    test({
+      code: 'import type { MyType } from "not-a-dependency";',
+      filename: testFilePath('./no-unused-modules/typescript/file-ts-a.ts'),
+      parser: require.resolve('babel-eslint'),
+    }),
+  ],
+  invalid: [
+  ],
+});
diff --git a/tests/src/rules/no-unresolved.js b/tests/src/rules/no-unresolved.js
index 9e6db8c04b..a5ff6da5d1 100644
--- a/tests/src/rules/no-unresolved.js
+++ b/tests/src/rules/no-unresolved.js
@@ -443,6 +443,7 @@ ruleTester.run('import() with built-in parser', rule, {
 });
 
 context('TypeScript', () => {
+  // Type-only imports were added in TypeScript ESTree 2.23.0
   getTSParsers().filter(x => x !== require.resolve('typescript-eslint-parser')).forEach((parser) => {
     ruleTester.run(`${parser}: no-unresolved ignore type-only`, rule, {
       valid: [
diff --git a/tests/src/rules/order.js b/tests/src/rules/order.js
index 146306259f..4b15cec898 100644
--- a/tests/src/rules/order.js
+++ b/tests/src/rules/order.js
@@ -2283,6 +2283,7 @@ ruleTester.run('order', rule, {
 
 context('TypeScript', function () {
   getNonDefaultParsers()
+    // Type-only imports were added in TypeScript ESTree 2.23.0
     .filter((parser) => parser !== require.resolve('typescript-eslint-parser'))
     .forEach((parser) => {
       const parserConfig = {