diff --git a/CHANGELOG.md b/CHANGELOG.md
index 97d2853..d993e8a 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -17,6 +17,7 @@
     even when TypeScript doesn't yet have a built-in type definition for them.
 * 💥 The type definitions now require TypeScript 3.5 or higher. ([#130](https://github.com/MattiasBuelens/web-streams-polyfill/pull/130))
 * 🐛 Prevent [warnings from Bluebird](http://bluebirdjs.com/docs/warning-explanations.html#warning-a-promise-was-created-in-a-handler-but-was-not-returned-from-it) about a promise being created within a handler but not being returned from a handler. ([#131](https://github.com/MattiasBuelens/web-streams-polyfill/pull/131))
+* 🏠 Improve internal `DOMException` polyfill. ([#133](https://github.com/MattiasBuelens/web-streams-polyfill/pull/133))
 
 ## v3.2.1 (2022-04-07)
 
diff --git a/src/stub/dom-exception.ts b/src/stub/dom-exception.ts
index 2a06a46..b676c8c 100644
--- a/src/stub/dom-exception.ts
+++ b/src/stub/dom-exception.ts
@@ -1,5 +1,6 @@
 /// <reference types="node" />
-import { NativeDOMException } from './native';
+import { globals } from '../globals';
+import { setFunctionName } from '../lib/helpers/miscellaneous';
 
 interface DOMException extends Error {
   name: string;
@@ -12,6 +13,9 @@ function isDOMExceptionConstructor(ctor: unknown): ctor is DOMExceptionConstruct
   if (!(typeof ctor === 'function' || typeof ctor === 'object')) {
     return false;
   }
+  if ((ctor as DOMExceptionConstructor).name !== 'DOMException') {
+    return false;
+  }
   try {
     new (ctor as DOMExceptionConstructor)();
     return true;
@@ -20,7 +24,21 @@ function isDOMExceptionConstructor(ctor: unknown): ctor is DOMExceptionConstruct
   }
 }
 
-function createDOMExceptionPolyfill(): DOMExceptionConstructor {
+/**
+ * Support:
+ * - Web browsers
+ * - Node 18 and higher (https://github.com/nodejs/node/commit/e4b1fb5e6422c1ff151234bb9de792d45dd88d87)
+ */
+function getFromGlobal(): DOMExceptionConstructor | undefined {
+  const ctor = globals?.DOMException;
+  return isDOMExceptionConstructor(ctor) ? ctor : undefined;
+}
+
+/**
+ * Support:
+ * - All platforms
+ */
+function createPolyfill(): DOMExceptionConstructor {
   // eslint-disable-next-line no-shadow
   const ctor = function DOMException(this: DOMException, message?: string, name?: string) {
     this.message = message || '';
@@ -29,13 +47,13 @@ function createDOMExceptionPolyfill(): DOMExceptionConstructor {
       Error.captureStackTrace(this, this.constructor);
     }
   } as any;
+  setFunctionName(ctor, 'DOMException');
   ctor.prototype = Object.create(Error.prototype);
   Object.defineProperty(ctor.prototype, 'constructor', { value: ctor, writable: true, configurable: true });
   return ctor;
 }
 
 // eslint-disable-next-line no-redeclare
-const DOMException: DOMExceptionConstructor =
-  isDOMExceptionConstructor(NativeDOMException) ? NativeDOMException : createDOMExceptionPolyfill();
+const DOMException: DOMExceptionConstructor = getFromGlobal() || createPolyfill();
 
 export { DOMException };
diff --git a/src/stub/native.ts b/src/stub/native.ts
deleted file mode 100644
index d76db48..0000000
--- a/src/stub/native.ts
+++ /dev/null
@@ -1,3 +0,0 @@
-/// <reference lib="dom" />
-export const NativeDOMException: typeof DOMException | undefined =
-  typeof DOMException !== 'undefined' ? DOMException : undefined;