diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index ede4f5d34371e8..8b085b3a9fda99 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -1176,7 +1176,7 @@ class Http2Session extends EventEmitter {
     // Otherwise, destroy immediately.
     if (!socket.destroyed) {
       if (!error) {
-        setImmediate(socket.end.bind(socket));
+        setImmediate(socket.destroy.bind(socket));
       } else {
         socket.destroy(error);
       }
diff --git a/test/parallel/test-http2-many-writes-and-destroy.js b/test/parallel/test-http2-many-writes-and-destroy.js
new file mode 100644
index 00000000000000..78db76e001cd3a
--- /dev/null
+++ b/test/parallel/test-http2-many-writes-and-destroy.js
@@ -0,0 +1,30 @@
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+const http2 = require('http2');
+
+{
+  const server = http2.createServer((req, res) => {
+    req.pipe(res);
+  });
+
+  server.listen(0, () => {
+    const url = `http://localhost:${server.address().port}`;
+    const client = http2.connect(url);
+    const req = client.request({ ':method': 'POST' });
+
+    for (let i = 0; i < 4000; i++) {
+      req.write(Buffer.alloc(6));
+    }
+
+    req.on('close', common.mustCall(() => {
+      console.log('(req onclose)');
+      server.close();
+      client.close();
+    }));
+
+    req.once('data', common.mustCall(() => req.destroy()));
+  });
+}
diff --git a/test/parallel/test-http2-pipe.js b/test/parallel/test-http2-pipe.js
index 2a759f9848721b..d7dd99df91edb5 100644
--- a/test/parallel/test-http2-pipe.js
+++ b/test/parallel/test-http2-pipe.js
@@ -33,6 +33,7 @@ server.listen(0, common.mustCall(() => {
   const client = http2.connect(`http://localhost:${server.address().port}`);
 
   const req = client.request({ ':method': 'POST' });
+
   req.on('response', common.mustCall());
   req.resume();
 
diff --git a/test/parallel/test-http2-server-close-callback.js b/test/parallel/test-http2-server-close-callback.js
new file mode 100644
index 00000000000000..66887aa62bebe5
--- /dev/null
+++ b/test/parallel/test-http2-server-close-callback.js
@@ -0,0 +1,24 @@
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+
+const http2 = require('http2');
+
+const server = http2.createServer();
+
+server.listen(0, common.mustCall(() => {
+  const client = http2.connect(`http://localhost:${server.address().port}`);
+  client.on('error', (err) => {
+    if (err.code !== 'ECONNRESET')
+      throw err;
+  });
+}));
+
+server.on('session', common.mustCall((s) => {
+  setImmediate(() => {
+    server.close(common.mustCall());
+    s.destroy();
+  });
+}));
diff --git a/test/parallel/test-http2-server-stream-session-destroy.js b/test/parallel/test-http2-server-stream-session-destroy.js
index 989c72ec959679..ef4f42fe39bc3a 100644
--- a/test/parallel/test-http2-server-stream-session-destroy.js
+++ b/test/parallel/test-http2-server-stream-session-destroy.js
@@ -44,10 +44,16 @@ server.on('stream', common.mustCall((stream) => {
 
 server.listen(0, common.mustCall(() => {
   const client = h2.connect(`http://localhost:${server.address().port}`);
-  client.on('error', () => {});
+  client.on('error', (err) => {
+    if (err.code !== 'ECONNRESET')
+      throw err;
+  });
   const req = client.request();
   req.resume();
   req.on('end', common.mustCall());
-  req.on('close', common.mustCall(() => server.close()));
-  req.on('error', () => {});
+  req.on('close', common.mustCall(() => server.close(common.mustCall())));
+  req.on('error', (err) => {
+    if (err.code !== 'ECONNRESET')
+      throw err;
+  });
 }));
diff --git a/test/parallel/test-http2-session-unref.js b/test/parallel/test-http2-session-unref.js
index e63cd0d208e32b..f946c2d3377b87 100644
--- a/test/parallel/test-http2-session-unref.js
+++ b/test/parallel/test-http2-session-unref.js
@@ -34,8 +34,11 @@ server.listen(0, common.mustCall(() => {
   // unref destroyed client
   {
     const client = http2.connect(`http://localhost:${port}`);
-    client.destroy();
-    client.unref();
+
+    client.on('connect', common.mustCall(() => {
+      client.destroy();
+      client.unref();
+    }));
   }
 
   // unref destroyed client
@@ -43,8 +46,11 @@ server.listen(0, common.mustCall(() => {
     const client = http2.connect(`http://localhost:${port}`, {
       createConnection: common.mustCall(() => clientSide)
     });
-    client.destroy();
-    client.unref();
+
+    client.on('connect', common.mustCall(() => {
+      client.destroy();
+      client.unref();
+    }));
   }
 }));
 server.emit('connection', serverSide);
diff --git a/test/sequential/test-http2-max-session-memory.js b/test/sequential/test-http2-max-session-memory.js
index d6d3bf935db801..644a20a3c88a50 100644
--- a/test/sequential/test-http2-max-session-memory.js
+++ b/test/sequential/test-http2-max-session-memory.js
@@ -13,6 +13,10 @@ const largeBuffer = Buffer.alloc(1e6);
 const server = http2.createServer({ maxSessionMemory: 1 });
 
 server.on('stream', common.mustCall((stream) => {
+  stream.on('error', (err) => {
+    if (err.code !== 'ECONNRESET')
+      throw err;
+  });
   stream.respond();
   stream.end(largeBuffer);
 }));