diff --git a/lib/_http_server.js b/lib/_http_server.js
index b728f73c419772..98aa53490946bd 100644
--- a/lib/_http_server.js
+++ b/lib/_http_server.js
@@ -29,7 +29,6 @@ const {
   ObjectSetPrototypeOf,
   ReflectApply,
   Symbol,
-  SymbolAsyncDispose,
   SymbolFor,
 } = primordials;
 
@@ -82,7 +81,6 @@ const {
 const {
   assignFunctionName,
   kEmptyObject,
-  promisify,
 } = require('internal/util');
 const {
   validateInteger,
@@ -580,10 +578,6 @@ Server.prototype.close = function close() {
   return this;
 };
 
-Server.prototype[SymbolAsyncDispose] = assignFunctionName(SymbolAsyncDispose, async function() {
-  await promisify(this.close).call(this);
-});
-
 Server.prototype.closeAllConnections = function closeAllConnections() {
   if (!this[kConnections]) {
     return;
diff --git a/lib/https.js b/lib/https.js
index acd3252b5cde66..e8cef0213d9876 100644
--- a/lib/https.js
+++ b/lib/https.js
@@ -33,13 +33,11 @@ const {
   ObjectSetPrototypeOf,
   ReflectApply,
   ReflectConstruct,
-  SymbolAsyncDispose,
 } = primordials;
 
 const {
   assertCrypto,
   kEmptyObject,
-  promisify,
 } = require('internal/util');
 assertCrypto();
 
@@ -116,10 +114,6 @@ Server.prototype.close = function close() {
   return this;
 };
 
-Server.prototype[SymbolAsyncDispose] = async function() {
-  await FunctionPrototypeCall(promisify(this.close), this);
-};
-
 /**
  * Creates a new `https.Server` instance.
  * @param {{
diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index 2ec1e9fc19a7e7..8fa5ccbf91870b 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -18,7 +18,6 @@ const {
   SafeMap,
   SafeSet,
   Symbol,
-  SymbolAsyncDispose,
   SymbolDispose,
   Uint32Array,
   Uint8Array,
@@ -3346,10 +3345,6 @@ class Http2Server extends NETServer {
     ReflectApply(NETServer.prototype.close, this, arguments);
     closeAllSessions(this);
   }
-
-  async [SymbolAsyncDispose]() {
-    await promisify(super.close).call(this);
-  }
 }
 
 Http2Server.prototype[EventEmitter.captureRejectionSymbol] = function(
diff --git a/lib/net.js b/lib/net.js
index a391e9da30f861..fa9f4d61d44622 100644
--- a/lib/net.js
+++ b/lib/net.js
@@ -118,6 +118,7 @@ const {
 const { isUint8Array } = require('internal/util/types');
 const { queueMicrotask } = require('internal/process/task_queues');
 const {
+  assignFunctionName,
   guessHandleType,
   isWindows,
   kEmptyObject,
@@ -2391,12 +2392,12 @@ Server.prototype.close = function(cb) {
   return this;
 };
 
-Server.prototype[SymbolAsyncDispose] = async function() {
+Server.prototype[SymbolAsyncDispose] = assignFunctionName(SymbolAsyncDispose, async function() {
   if (!this._handle) {
     return;
   }
   await FunctionPrototypeCall(promisify(this.close), this);
-};
+});
 
 Server.prototype._emitCloseIfDrained = function() {
   debug('SERVER _emitCloseIfDrained');
diff --git a/test/parallel/test-http-server-async-dispose.js b/test/parallel/test-http-server-async-dispose.js
index 8af11dcb7b0c3c..7ede8d7107a8f1 100644
--- a/test/parallel/test-http-server-async-dispose.js
+++ b/test/parallel/test-http-server-async-dispose.js
@@ -7,8 +7,12 @@ const { kConnectionsCheckingInterval } = require('_http_server');
 const server = createServer();
 
 server.listen(0, common.mustCall(() => {
+  assert.strictEqual(server[Symbol.asyncDispose].name, '[Symbol.asyncDispose]');
   server.on('close', common.mustCall());
   server[Symbol.asyncDispose]().then(common.mustCall(() => {
     assert(server[kConnectionsCheckingInterval]._destroyed);
+
+    // Disposer must be idempotent, subsequent call must not throw
+    server[Symbol.asyncDispose]().then(common.mustCall());
   }));
 }));
diff --git a/test/parallel/test-http2-server-async-dispose.js b/test/parallel/test-http2-server-async-dispose.js
index 4782e12e417d27..90456513d09fd0 100644
--- a/test/parallel/test-http2-server-async-dispose.js
+++ b/test/parallel/test-http2-server-async-dispose.js
@@ -6,10 +6,17 @@ if (!common.hasCrypto)
   common.skip('missing crypto');
 
 const http2 = require('http2');
+const assert = require('node:assert');
 
 const server = http2.createServer();
 
 server.listen(0, common.mustCall(() => {
+  assert.strictEqual(server[Symbol.asyncDispose].name, '[Symbol.asyncDispose]');
   server.on('close', common.mustCall());
-  server[Symbol.asyncDispose]().then(common.mustCall());
+  server[Symbol.asyncDispose]().then(common.mustCall(() => {
+    assert.strictEqual(server._handle, null);
+
+    // Disposer must be idempotent, subsequent call must not throw
+    server[Symbol.asyncDispose]().then(common.mustCall());
+  }));
 }));
diff --git a/test/parallel/test-https-server-async-dispose.js b/test/parallel/test-https-server-async-dispose.js
index 93b5cb74bbda11..6a88fde838e980 100644
--- a/test/parallel/test-https-server-async-dispose.js
+++ b/test/parallel/test-https-server-async-dispose.js
@@ -12,8 +12,12 @@ const { kConnectionsCheckingInterval } = require('_http_server');
 const server = createServer();
 
 server.listen(0, common.mustCall(() => {
+  assert.strictEqual(server[Symbol.asyncDispose].name, '[Symbol.asyncDispose]');
   server.on('close', common.mustCall());
   server[Symbol.asyncDispose]().then(common.mustCall(() => {
     assert(server[kConnectionsCheckingInterval]._destroyed);
+
+    // Disposer must be idempotent, subsequent call must not throw
+    server[Symbol.asyncDispose]().then(common.mustCall());
   }));
 }));