diff --git a/lib/internal/http2/compat.js b/lib/internal/http2/compat.js
index 88879484ebaab7..6e25b273018c92 100644
--- a/lib/internal/http2/compat.js
+++ b/lib/internal/http2/compat.js
@@ -260,6 +260,8 @@ class Http2ServerRequest extends Readable {
     stream[kRequest] = this;
 
     // Pause the stream..
+    stream.pause();
+    stream.on('data', onStreamData);
     stream.on('trailers', onStreamTrailers);
     stream.on('end', onStreamEnd);
     stream.on('error', onStreamError);
@@ -326,12 +328,8 @@ class Http2ServerRequest extends Readable {
   _read(nread) {
     const state = this[kState];
     if (!state.closed) {
-      if (!state.didRead) {
-        state.didRead = true;
-        this[kStream].on('data', onStreamData);
-      } else {
-        process.nextTick(resumeStream, this[kStream]);
-      }
+      state.didRead = true;
+      process.nextTick(resumeStream, this[kStream]);
     } else {
       this.emit('error', new ERR_HTTP2_INVALID_STREAM());
     }
diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index dfd74accabbd22..e7dbf9853fd49a 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -349,11 +349,11 @@ function onStreamClose(code) {
     // Push a null so the stream can end whenever the client consumes
     // it completely.
     stream.push(null);
-    // If the client hasn't tried to consume the stream and there is no
-    // resume scheduled (which would indicate they would consume in the future),
-    // then just dump the incoming data so that the stream can be destroyed.
-    if (!stream[kState].didRead && !stream._readableState.resumeScheduled)
-      stream.resume();
+
+    // Same as net.
+    if (stream.readableLength === 0) {
+      stream.read(0);
+    }
   }
 }
 
@@ -1795,8 +1795,6 @@ class Http2Stream extends Duplex {
     const ret = this[kHandle].trailers(headersList);
     if (ret < 0)
       this.destroy(new NghttpError(ret));
-    else
-      this[kMaybeDestroy]();
   }
 
   get closed() {
diff --git a/test/parallel/test-http2-client-upload-reject.js b/test/parallel/test-http2-client-upload-reject.js
index 678114130e3dba..ece7cbdf233f1f 100644
--- a/test/parallel/test-http2-client-upload-reject.js
+++ b/test/parallel/test-http2-client-upload-reject.js
@@ -20,15 +20,12 @@ fs.readFile(loc, common.mustCall((err, data) => {
   const server = http2.createServer();
 
   server.on('stream', common.mustCall((stream) => {
-    // Wait for some data to come through.
-    setImmediate(() => {
-      stream.on('close', common.mustCall(() => {
-        assert.strictEqual(stream.rstCode, 0);
-      }));
-
-      stream.respond({ ':status': 400 });
-      stream.end();
-    });
+    stream.on('close', common.mustCall(() => {
+      assert.strictEqual(stream.rstCode, 0);
+    }));
+
+    stream.respond({ ':status': 400 });
+    stream.end();
   }));
 
   server.listen(0, common.mustCall(() => {
diff --git a/test/parallel/test-http2-compat-client-upload-reject.js b/test/parallel/test-http2-compat-client-upload-reject.js
deleted file mode 100644
index e6a187cb12b264..00000000000000
--- a/test/parallel/test-http2-compat-client-upload-reject.js
+++ /dev/null
@@ -1,44 +0,0 @@
-'use strict';
-
-// Verifies that uploading data from a client works
-
-const common = require('../common');
-if (!common.hasCrypto)
-  common.skip('missing crypto');
-const assert = require('assert');
-const http2 = require('http2');
-const fs = require('fs');
-const fixtures = require('../common/fixtures');
-
-const loc = fixtures.path('person-large.jpg');
-
-assert(fs.existsSync(loc));
-
-fs.readFile(loc, common.mustCall((err, data) => {
-  assert.ifError(err);
-
-  const server = http2.createServer(common.mustCall((req, res) => {
-    setImmediate(() => {
-      res.writeHead(400);
-      res.end();
-    });
-  }));
-
-  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((headers) => {
-      assert.strictEqual(headers[':status'], 400);
-    }));
-
-    req.resume();
-    req.on('end', common.mustCall(() => {
-      server.close();
-      client.close();
-    }));
-
-    const str = fs.createReadStream(loc);
-    str.pipe(req);
-  }));
-}));