diff --git a/test/parallel/test-http2-compat-serverresponse-destroy.js b/test/parallel/test-http2-compat-serverresponse-destroy.js
new file mode 100644
index 00000000000000..40c73b0887c32f
--- /dev/null
+++ b/test/parallel/test-http2-compat-serverresponse-destroy.js
@@ -0,0 +1,91 @@
+// Flags: --expose-http2
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+const assert = require('assert');
+const http2 = require('http2');
+
+// Check that destroying the Http2ServerResponse stream produces
+// the expected result, including the ability to throw an error
+// which is emitted on server.streamError
+
+const errors = [
+  'test-error',
+  Error('test')
+];
+let nextError;
+
+const server = http2.createServer(common.mustCall((req, res) => {
+  req.on('error', common.mustNotCall());
+  res.on('error', common.mustNotCall());
+
+  res.on('finish', common.mustCall(() => {
+    assert.doesNotThrow(() => res.destroy(nextError));
+    assert.strictEqual(res.closed, true);
+  }));
+
+  if (req.path !== '/') {
+    nextError = errors.shift();
+  }
+  res.destroy(nextError);
+}, 3));
+
+server.on(
+  'streamError',
+  common.mustCall((err) => assert.strictEqual(err, nextError), 2)
+);
+
+server.listen(0, common.mustCall(() => {
+  const port = server.address().port;
+  const client = http2.connect(`http://localhost:${port}`);
+  const req = client.request({
+    ':path': '/',
+    ':method': 'GET',
+    ':scheme': 'http',
+    ':authority': `localhost:${port}`
+  });
+
+  req.on('response', common.mustNotCall());
+  req.on('error', common.mustNotCall());
+  req.on('end', common.mustCall());
+
+  req.resume();
+  req.end();
+
+  const req2 = client.request({
+    ':path': '/error',
+    ':method': 'GET',
+    ':scheme': 'http',
+    ':authority': `localhost:${port}`
+  });
+
+  req2.on('response', common.mustNotCall());
+  req2.on('error', common.mustNotCall());
+  req2.on('end', common.mustCall());
+
+  req2.resume();
+  req2.end();
+
+  const req3 = client.request({
+    ':path': '/error',
+    ':method': 'GET',
+    ':scheme': 'http',
+    ':authority': `localhost:${port}`
+  });
+
+  req3.on('response', common.mustNotCall());
+  req3.on('error', common.expectsError({
+    code: 'ERR_HTTP2_STREAM_ERROR',
+    type: Error,
+    message: 'Stream closed with error code 2'
+  }));
+  req3.on('end', common.mustCall(() => {
+    server.close();
+    client.destroy();
+  }));
+
+  req3.resume();
+  req3.end();
+}));
diff --git a/test/parallel/test-http2-compat-serverresponse-end.js b/test/parallel/test-http2-compat-serverresponse-end.js
index 5fb93e93dd5ff7..6c07f6d83e62e0 100644
--- a/test/parallel/test-http2-compat-serverresponse-end.js
+++ b/test/parallel/test-http2-compat-serverresponse-end.js
@@ -18,10 +18,12 @@ const {
   // Http2ServerResponse.end callback is called only the first time,
   // but may be invoked repeatedly without throwing errors.
   const server = createServer(mustCall((request, response) => {
+    strictEqual(response.closed, false);
     response.end(mustCall(() => {
       server.close();
     }));
     response.end(mustNotCall());
+    strictEqual(response.closed, true);
   }));
   server.listen(0, mustCall(() => {
     const { port } = server.address();
diff --git a/test/parallel/test-http2-compat-serverresponse-flushheaders.js b/test/parallel/test-http2-compat-serverresponse-flushheaders.js
index 671b0c7b94e661..f02732df87b050 100644
--- a/test/parallel/test-http2-compat-serverresponse-flushheaders.js
+++ b/test/parallel/test-http2-compat-serverresponse-flushheaders.js
@@ -15,8 +15,11 @@ const server = h2.createServer();
 server.listen(0, common.mustCall(function() {
   const port = server.address().port;
   server.once('request', common.mustCall(function(request, response) {
+    assert.strictEqual(response.headersSent, false);
     response.flushHeaders();
+    assert.strictEqual(response.headersSent, true);
     response.flushHeaders(); // Idempotent
+
     common.expectsError(() => {
       response.writeHead(400, { 'foo-bar': 'abc123' });
     }, {
diff --git a/test/parallel/test-http2-compat-serverresponse-headers.js b/test/parallel/test-http2-compat-serverresponse-headers.js
index 512a14c1c0cf8f..290c8a515fd2db 100644
--- a/test/parallel/test-http2-compat-serverresponse-headers.js
+++ b/test/parallel/test-http2-compat-serverresponse-headers.js
@@ -80,6 +80,10 @@ server.listen(0, common.mustCall(function() {
     response.getHeaders()[fake] = fake;
     assert.strictEqual(response.hasHeader(fake), false);
 
+    assert.strictEqual(response.sendDate, true);
+    response.sendDate = false;
+    assert.strictEqual(response.sendDate, false);
+
     response.on('finish', common.mustCall(function() {
       server.close();
     }));