diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index 9247292ff47fce..0b42bcd60c82ee 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -306,8 +306,23 @@ function onStreamClose(code) {
 
   if (state.fd !== undefined)
     tryClose(state.fd);
-  stream.push(null);
-  stream[kMaybeDestroy](null, code);
+
+  // Defer destroy we actually emit end.
+  if (stream._readableState.endEmitted || code !== NGHTTP2_NO_ERROR) {
+    // If errored or ended, we can destroy immediately.
+    stream[kMaybeDestroy](null, code);
+  } else {
+    // Wait for end to destroy.
+    stream.on('end', stream[kMaybeDestroy]);
+    // Push a null so the stream can end whenever the client consumes
+    // it completely.
+    stream.push(null);
+
+    // Same as net.
+    if (stream.readableLength === 0) {
+      stream.read(0);
+    }
+  }
 }
 
 // Receives a chunk of data for a given stream and forwards it on
@@ -325,11 +340,19 @@ function onStreamRead(nread, buf) {
     }
     return;
   }
+
   // Last chunk was received. End the readable side.
   debug(`Http2Stream ${stream[kID]} [Http2Session ` +
         `${sessionName(stream[kSession][kType])}]: ending readable.`);
-  stream.push(null);
-  stream[kMaybeDestroy]();
+
+  // defer this until we actually emit end
+  if (stream._readableState.endEmitted) {
+    stream[kMaybeDestroy]();
+  } else {
+    stream.on('end', stream[kMaybeDestroy]);
+    stream.push(null);
+    stream.read(0);
+  }
 }
 
 // Called when the remote peer settings have been updated.
@@ -1825,21 +1848,25 @@ class Http2Stream extends Duplex {
     session[kMaybeDestroy]();
     process.nextTick(emit, this, 'close', code);
     callback(err);
-  }
 
+  }
   // The Http2Stream can be destroyed if it has closed and if the readable
   // side has received the final chunk.
   [kMaybeDestroy](error, code = NGHTTP2_NO_ERROR) {
-    if (error == null) {
-      if (code === NGHTTP2_NO_ERROR &&
-          (!this._readableState.ended ||
-          !this._writableState.ended ||
-          this._writableState.pendingcb > 0 ||
-          !this.closed)) {
-        return;
-      }
+    if (error || code !== NGHTTP2_NO_ERROR) {
+      this.destroy(error);
+      return;
+    }
+
+    // TODO(mcollina): remove usage of _*State properties
+    if (this._readableState.ended &&
+        this._writableState.ended &&
+        this._writableState.pendingcb === 0 &&
+        this.closed) {
+      this.destroy();
+      // This should return, but eslint complains.
+      // return
     }
-    this.destroy(error);
   }
 }
 
diff --git a/test/parallel/test-http2-compat-short-stream-client-server.js b/test/parallel/test-http2-compat-short-stream-client-server.js
new file mode 100644
index 00000000000000..f7ef9412106f59
--- /dev/null
+++ b/test/parallel/test-http2-compat-short-stream-client-server.js
@@ -0,0 +1,50 @@
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+const assert = require('assert');
+const http2 = require('http2');
+const { Readable } = require('stream');
+
+const server = http2.createServer(common.mustCall((req, res) => {
+  res.setHeader('content-type', 'text/html');
+  const input = new Readable({
+    read() {
+      this.push('test');
+      this.push(null);
+    }
+  });
+  input.pipe(res);
+}));
+
+server.listen(0, common.mustCall(() => {
+  const port = server.address().port;
+  const client = http2.connect(`http://localhost:${port}`);
+
+  const req = client.request();
+
+  req.on('response', common.mustCall((headers) => {
+    assert.strictEqual(headers[':status'], 200);
+    assert.strictEqual(headers['content-type'], 'text/html');
+  }));
+
+  let data = '';
+
+  const notCallClose = common.mustNotCall();
+
+  setTimeout(() => {
+    req.setEncoding('utf8');
+    req.removeListener('close', notCallClose);
+    req.on('close', common.mustCall(() => {
+      server.close();
+      client.close();
+    }));
+    req.on('data', common.mustCallAtLeast((d) => data += d));
+    req.on('end', common.mustCall(() => {
+      assert.strictEqual(data, 'test');
+    }));
+  }, common.platformTimeout(100));
+
+  req.on('close', notCallClose);
+}));
diff --git a/test/parallel/test-http2-short-stream-client-server.js b/test/parallel/test-http2-short-stream-client-server.js
new file mode 100644
index 00000000000000..e632b8d96b9ea9
--- /dev/null
+++ b/test/parallel/test-http2-short-stream-client-server.js
@@ -0,0 +1,55 @@
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+const assert = require('assert');
+const http2 = require('http2');
+const { Readable } = require('stream');
+
+const server = http2.createServer();
+server.on('stream', common.mustCall((stream) => {
+  stream.respond({
+    ':status': 200,
+    'content-type': 'text/html'
+  });
+  const input = new Readable({
+    read() {
+      this.push('test');
+      this.push(null);
+    }
+  });
+  input.pipe(stream);
+}));
+
+
+server.listen(0, common.mustCall(() => {
+  const port = server.address().port;
+  const client = http2.connect(`http://localhost:${port}`);
+
+  const req = client.request();
+
+  req.on('response', common.mustCall((headers) => {
+    assert.strictEqual(headers[':status'], 200);
+    assert.strictEqual(headers['content-type'], 'text/html');
+  }));
+
+  let data = '';
+
+  const notCallClose = common.mustNotCall();
+
+  setTimeout(() => {
+    req.setEncoding('utf8');
+    req.removeListener('close', notCallClose);
+    req.on('close', common.mustCall(() => {
+      server.close();
+      client.close();
+    }));
+    req.on('data', common.mustCallAtLeast((d) => data += d));
+    req.on('end', common.mustCall(() => {
+      assert.strictEqual(data, 'test');
+    }));
+  }, common.platformTimeout(100));
+
+  req.on('close', notCallClose);
+}));