diff --git a/doc/api/stream.md b/doc/api/stream.md
index ba298cb4756ea9..35b23a966fff2d 100644
--- a/doc/api/stream.md
+++ b/doc/api/stream.md
@@ -618,6 +618,12 @@ instance, when the `readable.resume()` method is called without a listener
 attached to the `'data'` event, or when a `'data'` event handler is removed
 from the stream.
 
+Adding a [`'readable'`][] event handler automatically make the stream to
+stop flowing, and the data to be consumed via
+[`readable.read()`][stream-read]. If the [`'readable'`] event handler is
+removed, then the stream will start flowing again if there is a
+[`'data'`][] event handler.
+
 #### Three States
 
 The "two modes" of operation for a `Readable` stream are a simplified
@@ -666,12 +672,15 @@ within the streams internal buffer.
 The `Readable` stream API evolved across multiple Node.js versions and provides
 multiple methods of consuming stream data. In general, developers should choose
 *one* of the methods of consuming data and *should never* use multiple methods
-to consume data from a single stream.
+to consume data from a single stream. Specifically, using a combination
+of `on('data')`, `on('readable')`, `pipe()` or async iterators could
+lead to unintuitive behavior.
 
 Use of the `readable.pipe()` method is recommended for most users as it has been
 implemented to provide the easiest way of consuming stream data. Developers that
 require more fine-grained control over the transfer and generation of data can
-use the [`EventEmitter`][] and `readable.pause()`/`readable.resume()` APIs.
+use the [`EventEmitter`][] and `readable.on('readable')`/`readable.read()`
+or the `readable.pause()`/`readable.resume()` APIs.
 
 #### Class: stream.Readable
 <!-- YAML
@@ -825,7 +834,11 @@ result in increased throughput.
 
 If both `'readable'` and [`'data'`][]  are used at the same time, `'readable'`
 takes precedence in controlling the flow, i.e. `'data'` will be emitted
-only when [`stream.read()`][stream-read] is called.
+only when [`stream.read()`][stream-read] is called. The
+`readableFlowing` property would become `false`.
+If there are `'data'` listeners when `'readable'` is removed, the stream
+will start flowing, i.e. `'data'` events will be emitted without calling
+`.resume()`.
 
 ##### readable.destroy([error])
 <!-- YAML
@@ -887,6 +900,9 @@ readable.on('data', (chunk) => {
 });
 ```
 
+The `readable.pause()` method has no effect if there is a `'readable'`
+event listener.
+
 ##### readable.pipe(destination[, options])
 <!-- YAML
 added: v0.9.4
diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index 029faaa6142d96..f0829966438077 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -810,6 +810,7 @@ Readable.prototype.on = function(ev, fn) {
   } else if (ev === 'readable') {
     if (!state.endEmitted && !state.readableListening) {
       state.readableListening = state.needReadable = true;
+      state.flowing = false;
       state.emittedReadable = false;
       debug('on readable', state.length, state.reading);
       if (state.length) {
@@ -858,6 +859,11 @@ Readable.prototype.removeAllListeners = function(ev) {
 
 function updateReadableListening(self) {
   self._readableState.readableListening = self.listenerCount('readable') > 0;
+
+  // crude way to check if we should resume
+  if (self.listenerCount('data') > 0) {
+    self.resume();
+  }
 }
 
 function nReadingNextTick(self) {
@@ -872,7 +878,8 @@ Readable.prototype.resume = function() {
   if (!state.flowing) {
     debug('resume');
     // we flow only if there is no one listening
-    // for readable
+    // for readable, but we still have to call
+    // resume()
     state.flowing = !state.readableListening;
     resume(this, state);
   }
diff --git a/test/parallel/test-stream-once-readable-pipe.js b/test/parallel/test-stream-once-readable-pipe.js
new file mode 100644
index 00000000000000..e8f4e9422db401
--- /dev/null
+++ b/test/parallel/test-stream-once-readable-pipe.js
@@ -0,0 +1,61 @@
+'use strict';
+
+const common = require('../common');
+const assert = require('assert');
+const { Readable, Writable } = require('stream');
+
+// This test ensures that if have 'readable' listener
+// on Readable instance it will not disrupt the pipe.
+
+{
+  let receivedData = '';
+  const w = new Writable({
+    write: (chunk, env, callback) => {
+      receivedData += chunk;
+      callback();
+    },
+  });
+
+  const data = ['foo', 'bar', 'baz'];
+  const r = new Readable({
+    read: () => {},
+  });
+
+  r.once('readable', common.mustCall());
+
+  r.pipe(w);
+  r.push(data[0]);
+  r.push(data[1]);
+  r.push(data[2]);
+  r.push(null);
+
+  w.on('finish', common.mustCall(() => {
+    assert.strictEqual(receivedData, data.join(''));
+  }));
+}
+
+{
+  let receivedData = '';
+  const w = new Writable({
+    write: (chunk, env, callback) => {
+      receivedData += chunk;
+      callback();
+    },
+  });
+
+  const data = ['foo', 'bar', 'baz'];
+  const r = new Readable({
+    read: () => {},
+  });
+
+  r.pipe(w);
+  r.push(data[0]);
+  r.push(data[1]);
+  r.push(data[2]);
+  r.push(null);
+  r.once('readable', common.mustCall());
+
+  w.on('finish', common.mustCall(() => {
+    assert.strictEqual(receivedData, data.join(''));
+  }));
+}
diff --git a/test/parallel/test-stream-readable-reading-readingMore.js b/test/parallel/test-stream-readable-reading-readingMore.js
index 21361abc346555..71c07d7b062c18 100644
--- a/test/parallel/test-stream-readable-reading-readingMore.js
+++ b/test/parallel/test-stream-readable-reading-readingMore.js
@@ -31,10 +31,11 @@ const Readable = require('stream').Readable;
     assert.strictEqual(state.reading, false);
   }
 
+  const expectedReadingMore = [true, false];
   readable.on('readable', common.mustCall(() => {
-    // 'readable' always gets called before 'end'
-    // since 'end' hasn't been emitted, more data could be incoming
-    assert.strictEqual(state.readingMore, true);
+    // there is only one readingMore scheduled from on('data'),
+    // after which everything is governed by the .read() call
+    assert.strictEqual(state.readingMore, expectedReadingMore.shift());
 
     // if the stream has ended, we shouldn't be reading
     assert.strictEqual(state.ended, !state.reading);