diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index 2d69a21b4e3d02..0d23014760741b 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -681,12 +681,7 @@ Readable.prototype.pipe = function(dest, pipeOpts) {
     dest.end();
   }
 
-  // When the dest drains, it reduces the awaitDrain counter
-  // on the source.  This would be more elegant with a .once()
-  // handler in flow(), but adding and removing repeatedly is
-  // too slow.
-  const ondrain = pipeOnDrain(src);
-  dest.on('drain', ondrain);
+  let ondrain;
 
   var cleanedUp = false;
   function cleanup() {
@@ -694,7 +689,9 @@ Readable.prototype.pipe = function(dest, pipeOpts) {
     // Cleanup event handlers once the pipe is broken
     dest.removeListener('close', onclose);
     dest.removeListener('finish', onfinish);
-    dest.removeListener('drain', ondrain);
+    if (ondrain) {
+      dest.removeListener('drain', ondrain);
+    }
     dest.removeListener('error', onerror);
     dest.removeListener('unpipe', onunpipe);
     src.removeListener('end', onend);
@@ -708,7 +705,7 @@ Readable.prototype.pipe = function(dest, pipeOpts) {
     // flowing again.
     // So, if this is awaiting a drain, then we just call it now.
     // If we don't know, then assume that we are waiting for one.
-    if (state.awaitDrain &&
+    if (ondrain && state.awaitDrain &&
         (!dest._writableState || dest._writableState.needDrain))
       ondrain();
   }
@@ -729,6 +726,14 @@ Readable.prototype.pipe = function(dest, pipeOpts) {
         debug('false write response, pause', state.awaitDrain);
         state.awaitDrain++;
       }
+      if (!ondrain) {
+        // When the dest drains, it reduces the awaitDrain counter
+        // on the source.  This would be more elegant with a .once()
+        // handler in flow(), but adding and removing repeatedly is
+        // too slow.
+        ondrain = pipeOnDrain(src);
+        dest.on('drain', ondrain);
+      }
       src.pause();
     }
   }
diff --git a/test/parallel/test-stream-pipe-flow.js b/test/parallel/test-stream-pipe-flow.js
index b696821c0d51fb..1f2e8f54cec409 100644
--- a/test/parallel/test-stream-pipe-flow.js
+++ b/test/parallel/test-stream-pipe-flow.js
@@ -1,5 +1,6 @@
 'use strict';
 const common = require('../common');
+const assert = require('assert');
 const { Readable, Writable, PassThrough } = require('stream');
 
 {
@@ -65,3 +66,25 @@ const { Readable, Writable, PassThrough } = require('stream');
   wrapper.resume();
   wrapper.on('end', common.mustCall());
 }
+
+{
+  // Only register drain if there is backpressure.
+  const rs = new Readable({ read() {} });
+
+  const pt = rs
+    .pipe(new PassThrough({ objectMode: true, highWaterMark: 2 }));
+  assert.strictEqual(pt.listenerCount('drain'), 0);
+  pt.on('finish', () => {
+    assert.strictEqual(pt.listenerCount('drain'), 0);
+  });
+
+  rs.push('asd');
+  assert.strictEqual(pt.listenerCount('drain'), 0);
+
+  process.nextTick(() => {
+    rs.push('asd');
+    assert.strictEqual(pt.listenerCount('drain'), 0);
+    rs.push(null);
+    assert.strictEqual(pt.listenerCount('drain'), 0);
+  });
+}
diff --git a/test/parallel/test-stream2-readable-legacy-drain.js b/test/parallel/test-stream2-readable-legacy-drain.js
index 69780a078db216..beb36577766137 100644
--- a/test/parallel/test-stream2-readable-legacy-drain.js
+++ b/test/parallel/test-stream2-readable-legacy-drain.js
@@ -52,11 +52,4 @@ function drain() {
 
 w.end = common.mustCall();
 
-// Just for kicks, let's mess with the drain count.
-// This verifies that even if it gets negative in the
-// pipe() cleanup function, we'll still function properly.
-r.on('readable', function() {
-  w.emit('drain');
-});
-
 r.pipe(w);