diff --git a/lib/internal/streams/async_iterator.js b/lib/internal/streams/async_iterator.js
index 93b676ff02892b..5eefba517b97d2 100644
--- a/lib/internal/streams/async_iterator.js
+++ b/lib/internal/streams/async_iterator.js
@@ -22,6 +22,15 @@ const kStream = Symbol('stream');
 
 let Readable;
 
+function destroy(stream, err) {
+  // request.destroy just do .end - .abort is what we want
+  if (typeof stream.abort === 'function') return stream.abort();
+  if (stream.req &&
+      typeof stream.req.abort === 'function') return stream.req.abort();
+  if (typeof stream.destroy === 'function') return stream.destroy(err);
+  if (typeof stream.close === 'function') return stream.close();
+}
+
 function createIterResult(value, done) {
   return { value, done };
 }
@@ -141,7 +150,7 @@ const ReadableStreamAsyncIteratorPrototype = ObjectSetPrototypeOf({
           resolve(createIterResult(undefined, true));
         }
       });
-      stream.destroy();
+      destroy(stream);
     });
   },
 }, AsyncIteratorPrototype);
@@ -156,11 +165,7 @@ const createReadableStreamAsyncIterator = (stream) => {
 
     const src = stream;
     stream = new Readable({ objectMode: true }).wrap(src);
-    finished(stream, (err) => {
-      if (typeof src.destroy === 'function') {
-        src.destroy(err);
-      }
-    });
+    finished(stream, (err) => destroy(src, err));
   }
 
   const iterator = ObjectCreate(ReadableStreamAsyncIteratorPrototype, {
diff --git a/test/parallel/test-stream-readable-async-iterators.js b/test/parallel/test-stream-readable-async-iterators.js
index 26482fa717ef74..b783b5f2ee8440 100644
--- a/test/parallel/test-stream-readable-async-iterators.js
+++ b/test/parallel/test-stream-readable-async-iterators.js
@@ -56,6 +56,25 @@ async function tests() {
     }));
   }
 
+  {
+    // Non standard stream cleanup
+
+    const readable = new Readable({ autoDestroy: false, read() {} });
+    readable.push('asd');
+    readable.push('asd');
+    readable.destroy = null;
+    readable.close = common.mustCall(() => {
+      readable.emit('close');
+    });
+
+    await (async () => {
+      for await (const d of readable) {
+        d;
+        return;
+      }
+    })();
+  }
+
   {
     const readable = new Readable({ objectMode: true, read() {} });
     readable.push(0);