diff --git a/lib/dispatcher/client-h2.js b/lib/dispatcher/client-h2.js
index 7c8ec5f0cf9..cd63bcda2f2 100644
--- a/lib/dispatcher/client-h2.js
+++ b/lib/dispatcher/client-h2.js
@@ -208,10 +208,9 @@ function onHttp2SessionEnd () {
  * This is the root cause of #3011
  * We need to handle GOAWAY frames properly, and trigger the session close
  * along with the socket right away
- * Find a way to trigger the close cycle from here on.
  */
 function onHTTP2GoAway (code) {
-  const err = new InformationalError(`HTTP/2: "GOAWAY" frame received with code ${code}`)
+  const err = new RequestAbortedError(`HTTP/2: "GOAWAY" frame received with code ${code}`)
 
   // We need to trigger the close cycle right away
   // We need to destroy the session and the socket
@@ -220,8 +219,7 @@ function onHTTP2GoAway (code) {
   this[kClient][kOnError](err)
 
   this.unref()
-  // We send the GOAWAY frame response as no error
-  this.destroy()
+
   util.destroy(this[kSocket], err)
 }
 
diff --git a/lib/dispatcher/client.js b/lib/dispatcher/client.js
index 3b3da96d712..7d6f5fd351f 100644
--- a/lib/dispatcher/client.js
+++ b/lib/dispatcher/client.js
@@ -376,6 +376,7 @@ function onError (client, err) {
     assert(client[kPendingIdx] === client[kRunningIdx])
 
     const requests = client[kQueue].splice(client[kRunningIdx])
+
     for (let i = 0; i < requests.length; i++) {
       const request = requests[i]
       util.errorRequest(client, request, err)
diff --git a/test/http2.js b/test/http2.js
index 5d5badcc0f2..a43700574b8 100644
--- a/test/http2.js
+++ b/test/http2.js
@@ -234,7 +234,7 @@ test('Should support H2 GOAWAY (server-side)', async t => {
 
   server.on('session', session => {
     setTimeout(() => {
-      session.goaway(204)
+      session.goaway(0)
     }, 1000)
   })
 
@@ -274,7 +274,7 @@ test('Should support H2 GOAWAY (server-side)', async t => {
 
   t.ok(url instanceof URL)
   t.deepStrictEqual(disconnectClient, [client])
-  t.strictEqual(err.message, 'HTTP/2: "GOAWAY" frame received with code 204')
+  t.strictEqual(err.message, 'HTTP/2: "GOAWAY" frame received with code 0')
 })
 
 test('Should throw if bad allowH2 has been passed', async t => {
@@ -1427,20 +1427,21 @@ test('#3046 - GOAWAY Frame', async t => {
     t.strictEqual(err.message, 'HTTP/2: "GOAWAY" frame received with code 0')
   })
 
-  client.request({
+  const response = await client.request({
     path: '/',
     method: 'GET',
     headers: {
       'x-my-header': 'foo'
     }
-  }, (err, response) => {
-    t.ifError(err)
-    t.strictEqual(response.headers['content-type'], 'text/plain; charset=utf-8')
-    t.strictEqual(response.headers['x-custom-h2'], 'hello')
-    t.strictEqual(response.statusCode, 200)
-    // We stop the sent the GOAWAY frame before the body is sent, as we received the GOAWAY frame
-    // before the DATA one, the body will be empty
-    response.body.dump()
+  })
+
+  t.strictEqual(response.headers['content-type'], 'text/plain; charset=utf-8')
+  t.strictEqual(response.headers['x-custom-h2'], 'hello')
+  t.strictEqual(response.statusCode, 200)
+
+  t.rejects(response.body.text.bind(response.body), {
+    message: 'HTTP/2: "GOAWAY" frame received with code 0',
+    code: 'UND_ERR_ABORTED'
   })
 
   await t.completed