diff --git a/lib/internal/queue.js b/lib/internal/queue.js
index 01567aa5c..bb3e16b7c 100644
--- a/lib/internal/queue.js
+++ b/lib/internal/queue.js
@@ -45,27 +45,26 @@ export default function queue(worker, concurrency, payload) {
     }
 
     var processingScheduled = false;
-    function _insert(data, insertAtFront, callback) {
+    function _insert(data, insertAtFront, rejectOnError, callback) {
         if (callback != null && typeof callback !== 'function') {
             throw new Error('task callback must be a function');
         }
         q.started = true;
-        /*if (Array.isArray(data)) {
 
-            return data.map(datum => _insert(datum, insertAtFront, callback));
-        }*/
-
-        var res;
+        var res, rej;
+        function promiseCallback (err, ...args) {
+            // we don't care about the error, let the global error handler
+            // deal with it
+            if (err) return rejectOnError ? rej(err) : res()
+            if (args.length <= 1) return res(args[0])
+            res(args)
+        }
 
         var item = {
             data,
-            callback: callback || function (err, ...args) {
-                // we don't care about the error, let the global error handler
-                // deal with it
-                if (err) return
-                if (args.length <= 1) return res(args[0])
-                res(args)
-            }
+            callback: rejectOnError ?
+                promiseCallback :
+                (callback || promiseCallback)
         };
 
         if (insertAtFront) {
@@ -82,9 +81,10 @@ export default function queue(worker, concurrency, payload) {
             });
         }
 
-        if (!callback) {
-            return new Promise((resolve) => {
+        if (rejectOnError || !callback) {
+            return new Promise((resolve, reject) => {
                 res = resolve
+                rej = reject
             })
         }
     }
@@ -121,6 +121,15 @@ export default function queue(worker, concurrency, payload) {
         };
     }
 
+    function _maybeDrain(data) {
+        if (data.length === 0 && q.idle()) {
+            // call drain immediately if there are no tasks
+            setImmediate(() => trigger('drain'));
+            return true
+        }
+        return false
+    }
+
     const eventMethod = (name) => (handler) => {
         if (!handler) {
             return new Promise((resolve, reject) => {
@@ -148,13 +157,17 @@ export default function queue(worker, concurrency, payload) {
         paused: false,
         push (data, callback) {
             if (Array.isArray(data)) {
-                if (data.length === 0 && q.idle()) {
-                    // call drain immediately if there are no tasks
-                    return setImmediate(() => trigger('drain'));
-                }
-                return data.map(datum => _insert(datum, false, callback))
+                if (_maybeDrain(data)) return
+                return data.map(datum => _insert(datum, false, false, callback))
             }
-            return _insert(data, false, callback);
+            return _insert(data, false, false, callback);
+        },
+        pushAsync (data, callback) {
+            if (Array.isArray(data)) {
+                if (_maybeDrain(data)) return
+                return data.map(datum => _insert(datum, false, true, callback))
+            }
+            return _insert(data, false, true, callback);
         },
         kill () {
             off()
@@ -162,13 +175,17 @@ export default function queue(worker, concurrency, payload) {
         },
         unshift (data, callback) {
             if (Array.isArray(data)) {
-                if (data.length === 0 && q.idle()) {
-                    // call drain immediately if there are no tasks
-                    return setImmediate(() => trigger('drain'));
-                }
-                return data.map(datum => _insert(datum, true, callback))
+                if (_maybeDrain(data)) return
+                return data.map(datum => _insert(datum, true, false, callback))
+            }
+            return _insert(data, true, false, callback);
+        },
+        unshiftAsync (data, callback) {
+            if (Array.isArray(data)) {
+                if (_maybeDrain(data)) return
+                return data.map(datum => _insert(datum, true, true, callback))
             }
-            return _insert(data, true, callback);
+            return _insert(data, true, true, callback);
         },
         remove (testFn) {
             q._tasks.remove(testFn);
diff --git a/lib/queue.js b/lib/queue.js
index 53cf4ad62..dc5554735 100644
--- a/lib/queue.js
+++ b/lib/queue.js
@@ -21,12 +21,16 @@ import wrapAsync from './internal/wrapAsync';
  * @property {number} payload - an integer that specifies how many items are
  * passed to the worker function at a time. only applies if this is a
  * [cargo]{@link module:ControlFlow.cargo} object
- * @property {Function} push - add a new task to the `queue`. Calls `callback`
+ * @property {AsyncFunction} push - add a new task to the `queue`. Calls `callback`
  * once the `worker` has finished processing the task. Instead of a single task,
  * a `tasks` array can be submitted. The respective callback is used for every
  * task in the list. Invoke with `queue.push(task, [callback])`,
- * @property {Function} unshift - add a new task to the front of the `queue`.
+ * @property {AsyncFunction} unshift - add a new task to the front of the `queue`.
  * Invoke with `queue.unshift(task, [callback])`.
+ * @property {AsyncFunction} pushAsync - the same as `q.push`, except this returns
+ * a promise that rejects if an error occurs.
+ * @property {AsyncFunction} unshirtAsync - the same as `q.unshift`, except this returns
+ * a promise that rejects if an error occurs.
  * @property {Function} remove - remove items from the queue that match a test
  * function.  The test function will be passed an object with a `data` property,
  * and a `priority` property, if this is a
diff --git a/test/es2017/awaitableFunctions.js b/test/es2017/awaitableFunctions.js
index e8adf7b70..eb2663cff 100644
--- a/test/es2017/awaitableFunctions.js
+++ b/test/es2017/awaitableFunctions.js
@@ -618,6 +618,7 @@ module.exports = function () {
             'push cb 3',
             'push cb 4',
             'push cb 5',
+            'push cb undefined',
             'push cb 7',
             'unsaturated',
             'push cb 8'
diff --git a/test/queue.js b/test/queue.js
index e9f3a787d..f99e91af4 100644
--- a/test/queue.js
+++ b/test/queue.js
@@ -156,6 +156,46 @@ describe('queue', function(){
         });
     });
 
+    it('pushAsync', done => {
+        const calls = []
+        var q = async.queue((task, cb) => {
+            if (task === 2) return cb(new Error('fail'))
+            cb()
+        })
+
+        q.pushAsync(1, () => { throw new Error('should not be called') }).then(() => calls.push(1))
+        q.pushAsync(2).catch(err => {
+            expect(err.message).to.equal('fail')
+            calls.push(2)
+        })
+        q.pushAsync([3, 4]).map(p => p.then(() => calls.push('arr')))
+        q.drain(() => setTimeout(() => {
+            console.log('drain')
+            expect(calls).to.eql([1, 2, 'arr', 'arr'])
+            done()
+        }))
+    })
+
+    it('unshiftAsync', done => {
+        const calls = []
+        var q = async.queue((task, cb) => {
+            if (task === 2) return cb(new Error('fail'))
+            cb()
+        })
+
+        q.unshiftAsync(1).then(() => calls.push(1))
+        q.unshiftAsync(2).catch(err => {
+            expect(err.message).to.equal('fail')
+            calls.push(2)
+        })
+        q.unshiftAsync([3, 4]).map(p => p.then(() => calls.push('arr')))
+        q.drain(() => setTimeout(() => {
+            console.log('drain')
+            expect(calls).to.eql(['arr', 'arr', 2, 1])
+            done()
+        }))
+    })
+
     it('global error handler', (done) => {
         var results = [];