diff --git a/lib/6to5/modules/umd.js b/lib/6to5/modules/umd.js
index a9b4a02ca7..c727e4e939 100644
--- a/lib/6to5/modules/umd.js
+++ b/lib/6to5/modules/umd.js
@@ -43,6 +43,6 @@ UMDFormatter.prototype.transform = function (ast) {
 
   //
 
-  var call = b.callExpression(runner, [b.thisExpression(), factory]);
+  var call = b.callExpression(runner, [factory]);
   program.body = [b.expressionStatement(call)];
 };
diff --git a/lib/6to5/templates/umd-runner-body.js b/lib/6to5/templates/umd-runner-body.js
index b78bb97cb6..f3c9659b5b 100644
--- a/lib/6to5/templates/umd-runner-body.js
+++ b/lib/6to5/templates/umd-runner-body.js
@@ -1,4 +1,4 @@
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(AMD_ARGUMENTS, factory);
   } else if (typeof exports !== "undefined") {
diff --git a/test/fixtures/syntax/modules-umd/exports-default/expected.js b/test/fixtures/syntax/modules-umd/exports-default/expected.js
index 19c52b670d..a57b014819 100644
--- a/test/fixtures/syntax/modules-umd/exports-default/expected.js
+++ b/test/fixtures/syntax/modules-umd/exports-default/expected.js
@@ -1,12 +1,12 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports);
   }
-})(this, function (exports) {
+})(function (exports) {
   exports.default = 42;
   exports.default = {};
   exports.default = [];
diff --git a/test/fixtures/syntax/modules-umd/exports-from/expected.js b/test/fixtures/syntax/modules-umd/exports-from/expected.js
index a9eac93074..36887ea7cd 100644
--- a/test/fixtures/syntax/modules-umd/exports-from/expected.js
+++ b/test/fixtures/syntax/modules-umd/exports-from/expected.js
@@ -1,12 +1,12 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports", "foo"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports, require("foo"));
   }
-})(this, function (exports, _foo) {
+})(function (exports, _foo) {
   (function(obj) {
     for (var i in obj) {
       exports[i] = obj[i];
diff --git a/test/fixtures/syntax/modules-umd/exports-named/expected.js b/test/fixtures/syntax/modules-umd/exports-named/expected.js
index 8f40cd0dc3..8d48d6f6cd 100644
--- a/test/fixtures/syntax/modules-umd/exports-named/expected.js
+++ b/test/fixtures/syntax/modules-umd/exports-named/expected.js
@@ -1,12 +1,12 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports);
   }
-})(this, function (exports) {
+})(function (exports) {
   exports.foo = foo;
   exports.foo = foo;
   exports.bar = bar;
diff --git a/test/fixtures/syntax/modules-umd/exports-variable/expected.js b/test/fixtures/syntax/modules-umd/exports-variable/expected.js
index 32c11d7a54..aeb48672d5 100644
--- a/test/fixtures/syntax/modules-umd/exports-variable/expected.js
+++ b/test/fixtures/syntax/modules-umd/exports-variable/expected.js
@@ -1,12 +1,12 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports);
   }
-})(this, function (exports) {
+})(function (exports) {
   exports.foo7 = foo7;
   var foo = 1;
   exports.foo = foo;
diff --git a/test/fixtures/syntax/modules-umd/hoist-function-exports/expected.js b/test/fixtures/syntax/modules-umd/hoist-function-exports/expected.js
index bac912b1f6..914737417b 100644
--- a/test/fixtures/syntax/modules-umd/hoist-function-exports/expected.js
+++ b/test/fixtures/syntax/modules-umd/hoist-function-exports/expected.js
@@ -1,12 +1,12 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports", "./evens"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports, require("./evens"));
   }
-})(this, function (exports, _evens) {
+})(function (exports, _evens) {
   exports.nextOdd = nextOdd;
   var isEven = _evens.isEven;
 
diff --git a/test/fixtures/syntax/modules-umd/imports-default/expected.js b/test/fixtures/syntax/modules-umd/imports-default/expected.js
index 6acee23c2b..f2434dfe71 100644
--- a/test/fixtures/syntax/modules-umd/imports-default/expected.js
+++ b/test/fixtures/syntax/modules-umd/imports-default/expected.js
@@ -1,12 +1,12 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports", "foo"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports, require("foo"));
   }
-})(this, function (exports, _foo) {
+})(function (exports, _foo) {
   var foo = _foo.default;
   var foo = _foo.default;
 });
diff --git a/test/fixtures/syntax/modules-umd/imports-glob/expected.js b/test/fixtures/syntax/modules-umd/imports-glob/expected.js
index fb5a921da1..7dc4aeb30a 100644
--- a/test/fixtures/syntax/modules-umd/imports-glob/expected.js
+++ b/test/fixtures/syntax/modules-umd/imports-glob/expected.js
@@ -1,11 +1,11 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports", "foo"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports, require("foo"));
   }
-})(this, function (exports, _foo) {
+})(function (exports, _foo) {
   var foo = _foo;
 });
diff --git a/test/fixtures/syntax/modules-umd/imports-mixing/expected.js b/test/fixtures/syntax/modules-umd/imports-mixing/expected.js
index 102bd20f80..97f74e3918 100644
--- a/test/fixtures/syntax/modules-umd/imports-mixing/expected.js
+++ b/test/fixtures/syntax/modules-umd/imports-mixing/expected.js
@@ -1,12 +1,12 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports", "foo"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports, require("foo"));
   }
-})(this, function (exports, _foo) {
+})(function (exports, _foo) {
   var foo = _foo.default;
   var xyz = _foo.baz;
 });
diff --git a/test/fixtures/syntax/modules-umd/imports-named/expected.js b/test/fixtures/syntax/modules-umd/imports-named/expected.js
index ed10909514..896105f29c 100644
--- a/test/fixtures/syntax/modules-umd/imports-named/expected.js
+++ b/test/fixtures/syntax/modules-umd/imports-named/expected.js
@@ -1,12 +1,12 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports", "foo"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports, require("foo"));
   }
-})(this, function (exports, _foo) {
+})(function (exports, _foo) {
   var bar = _foo.bar;
   var bar = _foo.bar;
   var baz = _foo.baz;
diff --git a/test/fixtures/syntax/modules-umd/imports/expected.js b/test/fixtures/syntax/modules-umd/imports/expected.js
index 656e51677d..a80b499447 100644
--- a/test/fixtures/syntax/modules-umd/imports/expected.js
+++ b/test/fixtures/syntax/modules-umd/imports/expected.js
@@ -1,11 +1,11 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports", "foo", "foo-bar", "./directory/foo-bar"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports, require("foo"), require("foo-bar"), require("./directory/foo-bar"));
   }
-})(this, function (exports, _foo, _fooBar, _directoryFooBar) {
+})(function (exports, _foo, _fooBar, _directoryFooBar) {
 
 });
diff --git a/test/fixtures/syntax/modules-umd/overview/expected.js b/test/fixtures/syntax/modules-umd/overview/expected.js
index 475ce88de8..66095d379c 100644
--- a/test/fixtures/syntax/modules-umd/overview/expected.js
+++ b/test/fixtures/syntax/modules-umd/overview/expected.js
@@ -1,12 +1,12 @@
 "use strict";
 
-(function (root, factory) {
+(function (factory) {
   if (typeof define === "function" && define.amd) {
     define(["exports", "foo", "foo-bar", "./directory/foo-bar"], factory);
   } else if (typeof exports !== "undefined") {
     factory(exports, require("foo"), require("foo-bar"), require("./directory/foo-bar"));
   }
-})(this, function (exports, _foo, _fooBar, _directoryFooBar) {
+})(function (exports, _foo, _fooBar, _directoryFooBar) {
   var foo = _foo.default;
   var foo = _foo;
   var bar = _foo.bar;