diff --git a/es6-shim.js b/es6-shim.js
index ad82a093..3ab21af3 100644
--- a/es6-shim.js
+++ b/es6-shim.js
@@ -2965,11 +2965,12 @@
           if (arguments.length > 0) {
             addIterableToMap(Map, m, arguments[0]);
           }
+          delete m.constructor;
           Object.setPrototypeOf(m, globals.Map.prototype);
-          defineProperty(m, 'constructor', Map, true);
           return m;
         };
         globals.Map.prototype = create(OrigMapNoArgs.prototype);
+        defineProperty(globals.Map.prototype, 'constructor', globals.Map, true);
         Value.preserveToString(globals.Map, OrigMapNoArgs);
       }
       var testMap = new Map();
@@ -3053,11 +3054,12 @@
           if (arguments.length > 0) {
             addIterableToMap(Map, m, arguments[0]);
           }
+          delete m.constructor;
           Object.setPrototypeOf(m, Map.prototype);
-          defineProperty(m, 'constructor', Map, true);
           return m;
         };
         globals.Map.prototype = OrigMap.prototype;
+        defineProperty(globals.Map.prototype, 'constructor', globals.Map, true);
         Value.preserveToString(globals.Map, OrigMap);
       }
       var setSupportsSubclassing = supportsSubclassing(globals.Set, function (S) {
@@ -3083,11 +3085,12 @@
           if (arguments.length > 0) {
             addIterableToSet(Set, s, arguments[0]);
           }
+          delete s.constructor;
           Object.setPrototypeOf(s, Set.prototype);
-          defineProperty(s, 'constructor', Set, true);
           return s;
         };
         globals.Set.prototype = OrigSet.prototype;
+        defineProperty(globals.Set.prototype, 'constructor', globals.Set, true);
         Value.preserveToString(globals.Set, OrigSet);
       }
       var mapIterationThrowsStopIterator = !valueOrFalseIfThrows(function () {
diff --git a/test/collections.js b/test/collections.js
index 349090f3..7a48f34d 100644
--- a/test/collections.js
+++ b/test/collections.js
@@ -251,6 +251,12 @@ describe('Collections', function () {
       expectNotEnumerable(new Map());
     });
 
+    it('should not have an own constructor', function () {
+      var m = new Map();
+      expect(m).not.to.haveOwnPropertyDescriptor('constructor');
+      expect(m.constructor).to.equal(Map);
+    });
+
     it('should allow common ecmascript idioms', function () {
       expect(map).to.be.an.instanceOf(Map);
       expect(typeof Map.prototype.get).to.equal('function');
@@ -259,6 +265,10 @@ describe('Collections', function () {
       expect(typeof Map.prototype['delete']).to.equal('function');
     });
 
+    it('should have a unique constructor', function () {
+      expect(Map.prototype).to.not.equal(Object.prototype);
+    });
+
     describe('#clear()', function () {
       ifFunctionsHaveNamesIt('has the right name', function () {
         expect(Map.prototype.clear).to.have.property('name', 'clear');
@@ -351,10 +361,6 @@ describe('Collections', function () {
       });
     });
 
-    it('should has unique constructor', function () {
-      expect(Map.prototype).to.not.equal(Object.prototype);
-    });
-
     describe('#size', function () {
       it('throws TypeError when accessed directly', function () {
         // see https://github.com/paulmillr/es6-shim/issues/176
@@ -913,6 +919,12 @@ describe('Collections', function () {
       expectNotEnumerable(new Set());
     });
 
+    it('should not have an own constructor', function () {
+      var s = new Set();
+      expect(s).not.to.haveOwnPropertyDescriptor('constructor');
+      expect(s.constructor).to.equal(Set);
+    });
+
     it('should allow common ecmascript idioms', function () {
       expect(set instanceof Set).to.equal(true);
       expect(typeof Set.prototype.add).to.equal('function');
@@ -920,7 +932,7 @@ describe('Collections', function () {
       expect(typeof Set.prototype['delete']).to.equal('function');
     });
 
-    it('should has unique constructor', function () {
+    it('should have a unique constructor', function () {
       expect(Set.prototype).to.not.equal(Object.prototype);
     });