diff --git a/lib/dispatcher/client-h2.js b/lib/dispatcher/client-h2.js
index e8e78f99100..71cf1276a2b 100644
--- a/lib/dispatcher/client-h2.js
+++ b/lib/dispatcher/client-h2.js
@@ -26,7 +26,8 @@ const {
   kHTTP2Session,
   kResume,
   kSize,
-  kHTTPContext
+  kHTTPContext,
+  kClosed
 } = require('../core/symbols.js')
 
 const kOpenStreams = Symbol('open streams')
@@ -93,82 +94,37 @@ async function connectH2 (client, socket) {
   session[kOpenStreams] = 0
   session[kClient] = client
   session[kSocket] = socket
+  session[kHTTP2Session] = null
 
   util.addListener(session, 'error', onHttp2SessionError)
   util.addListener(session, 'frameError', onHttp2FrameError)
   util.addListener(session, 'end', onHttp2SessionEnd)
-  util.addListener(session, 'goaway', onHTTP2GoAway)
-  util.addListener(session, 'close', function () {
-    const { [kClient]: client } = this
-    const { [kSocket]: socket } = client
-
-    const err = this[kSocket][kError] || this[kError] || new SocketError('closed', util.getSocketInfo(socket))
-
-    client[kHTTP2Session] = null
-
-    if (client.destroyed) {
-      assert(client[kPending] === 0)
-
-      // Fail entire queue.
-      const requests = client[kQueue].splice(client[kRunningIdx])
-      for (let i = 0; i < requests.length; i++) {
-        const request = requests[i]
-        util.errorRequest(client, request, err)
-      }
-    }
-  })
+  util.addListener(session, 'goaway', onHttp2SessionGoAway)
+  util.addListener(session, 'close', onHttp2SessionClose)
 
   session.unref()
 
   client[kHTTP2Session] = session
   socket[kHTTP2Session] = session
 
-  util.addListener(socket, 'error', function (err) {
-    assert(err.code !== 'ERR_TLS_CERT_ALTNAME_INVALID')
-
-    this[kError] = err
-
-    this[kClient][kOnError](err)
-  })
-
-  util.addListener(socket, 'end', function () {
-    util.destroy(this, new SocketError('other side closed', util.getSocketInfo(this)))
-  })
-
-  util.addListener(socket, 'close', function () {
-    const err = this[kError] || new SocketError('closed', util.getSocketInfo(this))
-
-    client[kSocket] = null
+  util.addListener(socket, 'error', onHttp2SocketError)
+  util.addListener(socket, 'end', onHttp2SocketEnd)
+  util.addListener(socket, 'close', onHttp2SocketClose)
 
-    if (this[kHTTP2Session] != null) {
-      this[kHTTP2Session].destroy(err)
-    }
-
-    client[kPendingIdx] = client[kRunningIdx]
-
-    assert(client[kRunning] === 0)
-
-    client.emit('disconnect', client[kUrl], [client], err)
-
-    client[kResume]()
-  })
-
-  let closed = false
-  socket.on('close', () => {
-    closed = true
-  })
+  socket[kClosed] = false
+  socket.on('close', onSocketClose)
 
   return {
     version: 'h2',
     defaultPipelining: Infinity,
-    write (...args) {
-      return writeH2(client, ...args)
+    write (request) {
+      return writeH2(client, request)
     },
     resume () {
       resumeH2(client)
     },
     destroy (err, callback) {
-      if (closed) {
+      if (socket[kClosed]) {
         queueMicrotask(callback)
       } else {
         // Destroying the socket will trigger the session close
@@ -223,16 +179,19 @@ 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
+ *
+ * @this {import('http2').ClientHttp2Session}
+ * @param {number} errorCode
  */
-function onHTTP2GoAway (code) {
+function onHttp2SessionGoAway (errorCode) {
   // We cannot recover, so best to close the session and the socket
-  const err = this[kError] || new SocketError(`HTTP/2: "GOAWAY" frame received with code ${code}`, util.getSocketInfo(this))
+  const err = this[kError] || new SocketError(`HTTP/2: "GOAWAY" frame received with code ${errorCode}`, util.getSocketInfo(this[kSocket]))
   const client = this[kClient]
 
   client[kSocket] = null
   client[kHTTPContext] = null
 
-  if (this[kHTTP2Session] != null) {
+  if (this[kHTTP2Session] !== null) {
     this[kHTTP2Session].destroy(err)
     this[kHTTP2Session] = null
   }
@@ -253,6 +212,62 @@ function onHTTP2GoAway (code) {
   client[kResume]()
 }
 
+function onHttp2SessionClose () {
+  const { [kClient]: client } = this
+  const { [kSocket]: socket } = client
+
+  const err = this[kSocket][kError] || this[kError] || new SocketError('closed', util.getSocketInfo(socket))
+
+  client[kHTTP2Session] = null
+
+  if (client.destroyed) {
+    assert(client[kPending] === 0)
+
+    // Fail entire queue.
+    const requests = client[kQueue].splice(client[kRunningIdx])
+    for (let i = 0; i < requests.length; i++) {
+      const request = requests[i]
+      util.errorRequest(client, request, err)
+    }
+  }
+}
+
+function onHttp2SocketClose () {
+  const err = this[kError] || new SocketError('closed', util.getSocketInfo(this))
+
+  const client = this[kHTTP2Session][kClient]
+
+  client[kSocket] = null
+
+  if (this[kHTTP2Session] !== null) {
+    this[kHTTP2Session].destroy(err)
+  }
+
+  client[kPendingIdx] = client[kRunningIdx]
+
+  assert(client[kRunning] === 0)
+
+  client.emit('disconnect', client[kUrl], [client], err)
+
+  client[kResume]()
+}
+
+function onHttp2SocketError (err) {
+  assert(err.code !== 'ERR_TLS_CERT_ALTNAME_INVALID')
+
+  this[kError] = err
+
+  this[kClient][kOnError](err)
+}
+
+function onHttp2SocketEnd () {
+  util.destroy(this, new SocketError('other side closed', util.getSocketInfo(this)))
+}
+
+function onSocketClose () {
+  this[kClosed] = true
+}
+
 // https://www.rfc-editor.org/rfc/rfc7230#section-3.3.2
 function shouldSendContentLength (method) {
   return method !== 'GET' && method !== 'HEAD' && method !== 'OPTIONS' && method !== 'TRACE' && method !== 'CONNECT'