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..072eaf7b31 100644
--- a/tests/src/rules/max-dependencies.js
+++ b/tests/src/rules/max-dependencies.js
@@ -1,7 +1,7 @@
 import { test, getTSParsers } from '../utils';
 
 import { RuleTester } from 'eslint';
-import eslintPkg from 'eslint/package.json';
+import tsPkg from 'typescript/package.json';
 import semver from 'semver';
 
 const ruleTester = new RuleTester();
@@ -91,7 +91,7 @@ ruleTester.run('max-dependencies', rule, {
   ],
 });
 
-(semver.satisfies(eslintPkg.version, '>5.0.0') ? describe.skip : describe)('TypeScript', () => {
+(semver.satisfies(tsPkg.version, '>=3.8') ? describe.skip : describe)('TypeScript', () => {
   getTSParsers().forEach((parser) => {
     ruleTester.run(`max-dependencies (${parser.replace(process.cwd(), '.')})`, rule, {
       valid: [    
diff --git a/tests/src/rules/no-duplicates.js b/tests/src/rules/no-duplicates.js
index e550b63ce7..0fdfb2ae4b 100644
--- a/tests/src/rules/no-duplicates.js
+++ b/tests/src/rules/no-duplicates.js
@@ -4,6 +4,7 @@ import { test as testUtil, getNonDefaultParsers } from '../utils';
 import { RuleTester } from 'eslint';
 import eslintPkg from 'eslint/package.json';
 import semver from 'semver';
+import tsPkg from 'typescript/package.json';
 
 const ruleTester = new RuleTester();
 const rule = require('rules/no-duplicates');
@@ -415,9 +416,8 @@ import {x,y} from './foo'
   ],
 });
 
-context('TypeScript', function () {
+(semver.satisfies(tsPkg.version, '>=3.8') ? describe.skip : describe)('TypeScript', () => {
   getNonDefaultParsers()
-    .filter((parser) => parser !== require.resolve('typescript-eslint-parser'))
     .forEach((parser) => {
       const parserConfig = {
         parser,
diff --git a/tests/src/rules/no-extraneous-dependencies.js b/tests/src/rules/no-extraneous-dependencies.js
index 29604af170..046e120d34 100644
--- a/tests/src/rules/no-extraneous-dependencies.js
+++ b/tests/src/rules/no-extraneous-dependencies.js
@@ -3,7 +3,7 @@ import typescriptConfig from '../../../config/typescript';
 import path from 'path';
 import fs from 'fs';
 import semver from 'semver';
-import eslintPkg from 'eslint/package.json';
+import tsPkg from 'typescript/package.json';
 
 import { RuleTester } from 'eslint';
 import flatMap from 'array.prototype.flatmap';
@@ -380,8 +380,7 @@ 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', () => {
+(semver.satisfies(tsPkg.version, '>=3.8') ? describe.skip : describe)('TypeScript', () => {
   getTSParsers().forEach((parser) => {
     const parserConfig = {
       parser,
@@ -391,49 +390,27 @@ ruleTester.run('no-extraneous-dependencies', rule, {
       },
     };
 
-    if (parser !== require.resolve('typescript-eslint-parser')) {
-      ruleTester.run('no-extraneous-dependencies', rule, {
-        valid: [
-          test(Object.assign({
-            code: 'import type T from "a";',
-            options: [{ packageDir: packageDirWithTypescriptDevDependencies, devDependencies: false }],
-          }, parserConfig)),
-        ],
-        invalid: [
-          test(Object.assign({
-            code: 'import T from "a";',
-            options: [{ packageDir: packageDirWithTypescriptDevDependencies, devDependencies: false }],
-            errors: [{
-              message: "'a' should be listed in the project's dependencies, not devDependencies.",
-            }],
-          }, 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)),
-        ],
-      });
-    }
+    ruleTester.run('no-extraneous-dependencies', rule, {
+      valid: [
+        test(Object.assign({
+          code: 'import type T from "a";',
+          options: [{ packageDir: packageDirWithTypescriptDevDependencies, devDependencies: false }],
+        }, parserConfig)),
+      ],
+      invalid: [
+        test(Object.assign({
+          code: 'import T from "a";',
+          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')) {
+if (false && semver.satisfies(tsPkg.version, '>=3.8')) {
   typescriptRuleTester.run('no-extraneous-dependencies typescript type imports', rule, {
     valid: [
       test({
diff --git a/tests/src/rules/no-unresolved.js b/tests/src/rules/no-unresolved.js
index 9e6db8c04b..ce1a459d08 100644
--- a/tests/src/rules/no-unresolved.js
+++ b/tests/src/rules/no-unresolved.js
@@ -5,6 +5,8 @@ import { getTSParsers, test, SYNTAX_CASES, testVersion } from '../utils';
 import { CASE_SENSITIVE_FS } from 'eslint-module-utils/resolve';
 
 import { RuleTester } from 'eslint';
+import semver from 'semver';
+import tsPkg from 'typescript/package.json';
 
 const ruleTester = new RuleTester();
 const rule = require('rules/no-unresolved');
@@ -442,8 +444,8 @@ ruleTester.run('import() with built-in parser', rule, {
   ),
 });
 
-context('TypeScript', () => {
-  getTSParsers().filter(x => x !== require.resolve('typescript-eslint-parser')).forEach((parser) => {
+(semver.satisfies(tsPkg.version, '>=3.8') ? describe.skip : describe)('TypeScript', () => {
+  getTSParsers().forEach((parser) => {
     ruleTester.run(`${parser}: no-unresolved ignore type-only`, rule, {
       valid: [
         test({
diff --git a/tests/src/rules/order.js b/tests/src/rules/order.js
index 146306259f..1c47f2a9cf 100644
--- a/tests/src/rules/order.js
+++ b/tests/src/rules/order.js
@@ -3,6 +3,7 @@ import { test, getTSParsers, getNonDefaultParsers } from '../utils';
 import { RuleTester } from 'eslint';
 import eslintPkg from 'eslint/package.json';
 import semver from 'semver';
+import tsPkg from 'typescript/package.json';
 import flatMap from 'array.prototype.flatmap';
 
 const ruleTester = new RuleTester();
@@ -2281,9 +2282,8 @@ ruleTester.run('order', rule, {
 });
 
 
-context('TypeScript', function () {
+(semver.satisfies(tsPkg.version, '>=3.8') ? describe.skip : describe)('TypeScript', () => {
   getNonDefaultParsers()
-    .filter((parser) => parser !== require.resolve('typescript-eslint-parser'))
     .forEach((parser) => {
       const parserConfig = {
         parser,