diff --git a/src/ng/rootScope.js b/src/ng/rootScope.js
index 85c04376b2f5..f2fbec1a1c61 100644
--- a/src/ng/rootScope.js
+++ b/src/ng/rootScope.js
@@ -1207,7 +1207,10 @@ function $RootScopeProvider() {
         return function() {
           var indexOfListener = namedListeners.indexOf(listener);
           if (indexOfListener !== -1) {
-            namedListeners[indexOfListener] = null;
+            // Use delete in the hope of the browser deallocating the memory for the array entry,
+            // while not shifting the array indexes of other listeners.
+            // See issue https://github.com/angular/angular.js/issues/16135
+            delete namedListeners[indexOfListener];
             decrementListenerCount(self, 1, name);
           }
         };
diff --git a/test/ng/rootScopeSpec.js b/test/ng/rootScopeSpec.js
index dd1a23f20625..83005e674cbc 100644
--- a/test/ng/rootScopeSpec.js
+++ b/test/ng/rootScopeSpec.js
@@ -1903,6 +1903,21 @@ describe('Scope', function() {
         }));
 
 
+        // See issue https://github.com/angular/angular.js/issues/16135
+        it('should deallocate the listener array entry', inject(function($rootScope) {
+          var remove1 = $rootScope.$on('abc', noop);
+          $rootScope.$on('abc', noop);
+
+          expect($rootScope.$$listeners['abc'].length).toBe(2);
+          expect(0 in $rootScope.$$listeners['abc']).toBe(true);
+
+          remove1();
+
+          expect($rootScope.$$listeners['abc'].length).toBe(2);
+          expect(0 in $rootScope.$$listeners['abc']).toBe(false);
+        }));
+
+
         it('should call next listener after removing the current listener via its own handler', inject(function($rootScope) {
           var listener1 = jasmine.createSpy('listener1').and.callFake(function() { remove1(); });
           var remove1 = $rootScope.$on('abc', listener1);