diff --git a/packages/babel-plugin-transform-es2015-modules-umd/README.md b/packages/babel-plugin-transform-es2015-modules-umd/README.md
index cfcdc5b359..9af5b210c0 100644
--- a/packages/babel-plugin-transform-es2015-modules-umd/README.md
+++ b/packages/babel-plugin-transform-es2015-modules-umd/README.md
@@ -20,9 +20,9 @@ $ npm install babel-plugin-transform-es2015-modules-umd
 
 You can also override the names of particular libraries when this module is
 running in the browser.  For example the `es6-promise` library exposes itself
-as `global.Promise` rather than `global.es6Promise`. This can be accomidated by:
+as `global.Promise` rather than `global.es6Promise`. This can be accommodated by:
 
-```
+```json
 {
   "plugins": [
     ["transform-es2015-modules-umd", {
@@ -34,6 +34,135 @@ as `global.Promise` rather than `global.es6Promise`. This can be accomidated by:
 }
 ```
 
+#### Default semantics
+
+There are a few things to note about the default semantics.
+
+_First_, this transform uses the
+[basename](https://en.wikipedia.org/wiki/Basename) of each import to generate
+the global names in the UMD output. This means that if you're importing
+multiple modules with the same basename, like:
+
+```js
+import fooBar1 from "foo-bar";
+import fooBar2 from "./mylib/foo-bar";
+```
+
+it will transpile into two references to the same browser global:
+
+```js
+factory(global.fooBar, global.fooBar);
+```
+
+If you set the plugin options to:
+
+```json
+{
+  "globals": {
+    "foo-bar": "fooBAR",
+    "./mylib/foo-bar": "mylib.fooBar"
+  }
+}
+```
+
+it will still transpile both to one browser global:
+
+```js
+factory(global.fooBAR, global.fooBAR);
+```
+
+because again the transform is only using the basename of the import.
+
+_Second_, the specified override will still be passed to the `toIdentifier`
+function in [babel-types/src/converters](../babel-types/src/converters.js).
+This means that if you specify an override as a member expression like:
+
+```json
+{
+  "globals": {
+    "fizzbuzz": "fizz.buzz"
+  }
+}
+```
+
+this will _not_ transpile to `factory(global.fizz.buzz)`. Instead, it will
+transpile to `factory(global.fizzBuzz)` based on the logic in `toIdentifier`.
+
+_Third_, you cannot override the exported global name.
+
+#### More flexible semantics with `exactGlobals: true`
+
+All of these behaviors can limit the flexibility of the `globals` map. To
+remove these limitations, you can set the `exactGlobals` option to `true`.
+Doing this instructs the plugin to:
+
+1. always use the full import string instead of the basename when generating
+the global names
+2. skip passing `globals` overrides to the `toIdentifier` function. Instead,
+they are used exactly as written, so you will get errors if you do not use
+valid identifiers or valid uncomputed (dot) member expressions.
+3. allow the exported global name to be overridden via the `globals` map. Any
+override must again be a valid identifier or valid member expression.
+
+Thus, if you set `exactGlobals` to `true` and do not pass any overrides, the
+first example of:
+
+```js
+import fooBar1 from "foo-bar";
+import fooBar2 from "./mylib/foo-bar";
+```
+
+will transpile to:
+
+```js
+factory(global.fooBar, global.mylibFooBar);
+```
+
+And if you set the plugin options to:
+
+```json
+{
+  "globals": {
+    "foo-bar": "fooBAR",
+    "./mylib/foo-bar": "mylib.fooBar"
+  },
+  "exactGlobals": true
+}
+```
+
+then it'll transpile to:
+
+```js
+factory(global.fooBAR, global.mylib.fooBar)
+```
+
+Finally, with the plugin options set to:
+
+```json
+{
+  "plugins": [
+    "external-helpers",
+    ["transform-es2015-modules-umd", {
+      "globals": {
+        "my/custom/module/name": "My.Custom.Module.Name"
+      },
+      "exactGlobals": true
+    }]
+  ],
+  "moduleId": "my/custom/module/name"
+}
+```
+
+it will transpile to:
+
+```js
+factory(mod.exports);
+global.My = global.My || {};
+global.My.Custom = global.My.Custom || {};
+global.My.Custom.Module = global.My.Custom.Module || {};
+global.My.Custom.Module.Name = mod.exports;
+```
+
 ### Via CLI
 
 ```sh
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/src/index.js b/packages/babel-plugin-transform-es2015-modules-umd/src/index.js
index 26b59f19d0..44b88ee55d 100644
--- a/packages/babel-plugin-transform-es2015-modules-umd/src/index.js
+++ b/packages/babel-plugin-transform-es2015-modules-umd/src/index.js
@@ -3,6 +3,17 @@
 import { basename, extname } from "path";
 import template from "babel-template";
 
+let buildPrerequisiteAssignment = template(`
+  GLOBAL_REFERENCE = GLOBAL_REFERENCE || {}
+`);
+
+let buildGlobalExport = template(`
+  var mod = { exports: {} };
+  factory(BROWSER_ARGUMENTS);
+  PREREQUISITE_ASSIGNMENTS
+  GLOBAL_TO_ASSIGN = mod.exports;
+`);
+
 let buildWrapper = template(`
   (function (global, factory) {
     if (typeof define === "function" && define.amd) {
@@ -10,9 +21,7 @@ let buildWrapper = template(`
     } else if (typeof exports !== "undefined") {
       factory(COMMON_ARGUMENTS);
     } else {
-      var mod = { exports: {} };
-      factory(BROWSER_ARGUMENTS);
-      global.GLOBAL_ARG = mod.exports;
+      GLOBAL_EXPORT
     }
   })(this, FUNC);
 `);
@@ -65,23 +74,62 @@ export default function ({ types: t }) {
             } else if (arg.value === "exports") {
               return t.memberExpression(t.identifier("mod"), t.identifier("exports"));
             } else {
-              let requireName = basename(arg.value, extname(arg.value));
-              let globalName = browserGlobals[requireName] || requireName;
+              let memberExpression;
 
-              return t.memberExpression(t.identifier("global"), t.identifier(
-                t.toIdentifier(globalName)
-              ));
+              if (state.opts.exactGlobals) {
+                let globalRef = browserGlobals[arg.value];
+                if (globalRef) {
+                  memberExpression = globalRef.split(".").reduce(
+                    (accum, curr) => t.memberExpression(accum, t.identifier(curr)), t.identifier("global")
+                  );
+                } else {
+                  memberExpression = t.memberExpression(
+                    t.identifier("global"), t.identifier(t.toIdentifier(arg.value))
+                  );
+                }
+              } else {
+                let requireName = basename(arg.value, extname(arg.value));
+                let globalName = browserGlobals[requireName] || requireName;
+                memberExpression = t.memberExpression(
+                  t.identifier("global"), t.identifier(t.toIdentifier(globalName))
+                );
+              }
+
+              return memberExpression;
             }
           });
 
-          let globalArg = t.identifier(t.toIdentifier(moduleName ? moduleName.value : this.file.opts.basename));
+          let moduleNameOrBasename = moduleName ? moduleName.value : this.file.opts.basename;
+          let globalToAssign = t.memberExpression(
+            t.identifier("global"), t.identifier(t.toIdentifier(moduleNameOrBasename))
+          );
+          let prerequisiteAssignments = null;
+
+          if (state.opts.exactGlobals) {
+            let globalName = browserGlobals[moduleNameOrBasename];
+
+            if (globalName) {
+              prerequisiteAssignments = [];
+
+              let members = globalName.split(".");
+              globalToAssign = members.slice(1).reduce((accum, curr) => {
+                prerequisiteAssignments.push(buildPrerequisiteAssignment({ GLOBAL_REFERENCE: accum }));
+                return t.memberExpression(accum, t.identifier(curr));
+              }, t.memberExpression(t.identifier("global"), t.identifier(members[0])));
+            }
+          }
+
+          let globalExport = buildGlobalExport({
+            BROWSER_ARGUMENTS: browserArgs,
+            PREREQUISITE_ASSIGNMENTS: prerequisiteAssignments,
+            GLOBAL_TO_ASSIGN: globalToAssign
+          });
 
           last.replaceWith(buildWrapper({
             MODULE_NAME: moduleName,
-            BROWSER_ARGUMENTS: browserArgs,
             AMD_ARGUMENTS: amdArgs,
             COMMON_ARGUMENTS: commonArgs,
-            GLOBAL_ARG: globalArg,
+            GLOBAL_EXPORT: globalExport,
             FUNC: func
           }));
         }
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false-with-overrides/actual.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false-with-overrides/actual.js
new file mode 100644
index 0000000000..0e67018dc4
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false-with-overrides/actual.js
@@ -0,0 +1,3 @@
+import fooBar1 from "foo-bar";
+import fooBar2 from "./mylib/foo-bar";
+import fizzBuzz from "fizzbuzz";
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false-with-overrides/expected.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false-with-overrides/expected.js
new file mode 100644
index 0000000000..5bb49994e0
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false-with-overrides/expected.js
@@ -0,0 +1,21 @@
+(function (global, factory) {
+  if (typeof define === "function" && define.amd) {
+    define(["foo-bar", "./mylib/foo-bar", "fizzbuzz"], factory);
+  } else if (typeof exports !== "undefined") {
+    factory(require("foo-bar"), require("./mylib/foo-bar"), require("fizzbuzz"));
+  } else {
+    var mod = {
+      exports: {}
+    };
+    factory(global.fooBAR, global.fooBAR, global.fizzBuzz);
+    global.actual = mod.exports;
+  }
+})(this, function (_fooBar, _fooBar3, _fizzbuzz) {
+  "use strict";
+
+  var _fooBar2 = babelHelpers.interopRequireDefault(_fooBar);
+
+  var _fooBar4 = babelHelpers.interopRequireDefault(_fooBar3);
+
+  var _fizzbuzz2 = babelHelpers.interopRequireDefault(_fizzbuzz);
+});
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false-with-overrides/options.json b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false-with-overrides/options.json
new file mode 100644
index 0000000000..e15ffb81e0
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false-with-overrides/options.json
@@ -0,0 +1,12 @@
+{
+  "plugins": [
+    "external-helpers",
+    ["transform-es2015-modules-umd", {
+      "globals": {
+        "foo-bar": "fooBAR",
+        "./mylib/foo-bar": "mylib.fooBar",
+        "fizzbuzz": "fizz.buzz"
+      }
+    }]
+  ]
+}
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false/actual.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false/actual.js
new file mode 100644
index 0000000000..0e67018dc4
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false/actual.js
@@ -0,0 +1,3 @@
+import fooBar1 from "foo-bar";
+import fooBar2 from "./mylib/foo-bar";
+import fizzBuzz from "fizzbuzz";
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false/expected.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false/expected.js
new file mode 100644
index 0000000000..527e2f698b
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-false/expected.js
@@ -0,0 +1,21 @@
+(function (global, factory) {
+  if (typeof define === "function" && define.amd) {
+    define(["foo-bar", "./mylib/foo-bar", "fizzbuzz"], factory);
+  } else if (typeof exports !== "undefined") {
+    factory(require("foo-bar"), require("./mylib/foo-bar"), require("fizzbuzz"));
+  } else {
+    var mod = {
+      exports: {}
+    };
+    factory(global.fooBar, global.fooBar, global.fizzbuzz);
+    global.actual = mod.exports;
+  }
+})(this, function (_fooBar, _fooBar3, _fizzbuzz) {
+  "use strict";
+
+  var _fooBar2 = babelHelpers.interopRequireDefault(_fooBar);
+
+  var _fooBar4 = babelHelpers.interopRequireDefault(_fooBar3);
+
+  var _fizzbuzz2 = babelHelpers.interopRequireDefault(_fizzbuzz);
+});
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true-with-overrides/actual.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true-with-overrides/actual.js
new file mode 100644
index 0000000000..0e67018dc4
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true-with-overrides/actual.js
@@ -0,0 +1,3 @@
+import fooBar1 from "foo-bar";
+import fooBar2 from "./mylib/foo-bar";
+import fizzBuzz from "fizzbuzz";
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true-with-overrides/expected.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true-with-overrides/expected.js
new file mode 100644
index 0000000000..702163cd78
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true-with-overrides/expected.js
@@ -0,0 +1,21 @@
+(function (global, factory) {
+  if (typeof define === "function" && define.amd) {
+    define(["foo-bar", "./mylib/foo-bar", "fizzbuzz"], factory);
+  } else if (typeof exports !== "undefined") {
+    factory(require("foo-bar"), require("./mylib/foo-bar"), require("fizzbuzz"));
+  } else {
+    var mod = {
+      exports: {}
+    };
+    factory(global.fooBAR, global.mylib.fooBar, global.fizz.buzz);
+    global.actual = mod.exports;
+  }
+})(this, function (_fooBar, _fooBar3, _fizzbuzz) {
+  "use strict";
+
+  var _fooBar2 = babelHelpers.interopRequireDefault(_fooBar);
+
+  var _fooBar4 = babelHelpers.interopRequireDefault(_fooBar3);
+
+  var _fizzbuzz2 = babelHelpers.interopRequireDefault(_fizzbuzz);
+});
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true-with-overrides/options.json b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true-with-overrides/options.json
new file mode 100644
index 0000000000..01e37b5b27
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true-with-overrides/options.json
@@ -0,0 +1,13 @@
+{
+  "plugins": [
+    "external-helpers",
+    ["transform-es2015-modules-umd", {
+      "globals": {
+        "foo-bar": "fooBAR",
+        "./mylib/foo-bar": "mylib.fooBar",
+        "fizzbuzz": "fizz.buzz"
+      },
+      "exactGlobals": true
+    }]
+  ]
+}
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true/actual.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true/actual.js
new file mode 100644
index 0000000000..0e67018dc4
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true/actual.js
@@ -0,0 +1,3 @@
+import fooBar1 from "foo-bar";
+import fooBar2 from "./mylib/foo-bar";
+import fizzBuzz from "fizzbuzz";
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true/expected.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true/expected.js
new file mode 100644
index 0000000000..990ac8401f
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true/expected.js
@@ -0,0 +1,21 @@
+(function (global, factory) {
+  if (typeof define === "function" && define.amd) {
+    define(["foo-bar", "./mylib/foo-bar", "fizzbuzz"], factory);
+  } else if (typeof exports !== "undefined") {
+    factory(require("foo-bar"), require("./mylib/foo-bar"), require("fizzbuzz"));
+  } else {
+    var mod = {
+      exports: {}
+    };
+    factory(global.fooBar, global.mylibFooBar, global.fizzbuzz);
+    global.actual = mod.exports;
+  }
+})(this, function (_fooBar, _fooBar3, _fizzbuzz) {
+  "use strict";
+
+  var _fooBar2 = babelHelpers.interopRequireDefault(_fooBar);
+
+  var _fooBar4 = babelHelpers.interopRequireDefault(_fooBar3);
+
+  var _fizzbuzz2 = babelHelpers.interopRequireDefault(_fizzbuzz);
+});
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true/options.json b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true/options.json
new file mode 100644
index 0000000000..3ac7220822
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/imports-exact-globals-true/options.json
@@ -0,0 +1,8 @@
+{
+  "plugins": [
+    "external-helpers",
+    ["transform-es2015-modules-umd", {
+      "exactGlobals": true
+    }]
+  ]
+}
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-namespace/actual.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-namespace/actual.js
new file mode 100644
index 0000000000..7a4e8a723a
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-namespace/actual.js
@@ -0,0 +1 @@
+export default 42;
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-namespace/expected.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-namespace/expected.js
new file mode 100644
index 0000000000..9000a0b8bd
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-namespace/expected.js
@@ -0,0 +1,21 @@
+(function (global, factory) {
+  if (typeof define === "function" && define.amd) {
+    define("my custom module name", ["exports"], factory);
+  } else if (typeof exports !== "undefined") {
+    factory(exports);
+  } else {
+    var mod = {
+      exports: {}
+    };
+    factory(mod.exports);
+    global.foo = global.foo || {};
+    global.foo.bar = mod.exports;
+  }
+})(this, function (exports) {
+  "use strict";
+
+  Object.defineProperty(exports, "__esModule", {
+    value: true
+  });
+  exports.default = 42;
+});
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-namespace/options.json b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-namespace/options.json
new file mode 100644
index 0000000000..23eb69e3b8
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-namespace/options.json
@@ -0,0 +1,12 @@
+{
+  "plugins": [
+    "external-helpers",
+    ["transform-es2015-modules-umd", {
+      "globals": {
+        "my custom module name": "foo.bar"
+      },
+      "exactGlobals": true
+    }]
+  ],
+  "moduleId": "my custom module name"
+}
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-very-nested-namespace/actual.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-very-nested-namespace/actual.js
new file mode 100644
index 0000000000..7a4e8a723a
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-very-nested-namespace/actual.js
@@ -0,0 +1 @@
+export default 42;
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-very-nested-namespace/expected.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-very-nested-namespace/expected.js
new file mode 100644
index 0000000000..52ab4409c0
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-very-nested-namespace/expected.js
@@ -0,0 +1,23 @@
+(function (global, factory) {
+  if (typeof define === "function" && define.amd) {
+    define("my custom module name", ["exports"], factory);
+  } else if (typeof exports !== "undefined") {
+    factory(exports);
+  } else {
+    var mod = {
+      exports: {}
+    };
+    factory(mod.exports);
+    global.foo = global.foo || {};
+    global.foo.bar = global.foo.bar || {};
+    global.foo.bar.baz = global.foo.bar.baz || {};
+    global.foo.bar.baz.qux = mod.exports;
+  }
+})(this, function (exports) {
+  "use strict";
+
+  Object.defineProperty(exports, "__esModule", {
+    value: true
+  });
+  exports.default = 42;
+});
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-very-nested-namespace/options.json b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-very-nested-namespace/options.json
new file mode 100644
index 0000000000..ad97739f25
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global-in-very-nested-namespace/options.json
@@ -0,0 +1,12 @@
+{
+  "plugins": [
+    "external-helpers",
+    ["transform-es2015-modules-umd", {
+      "globals": {
+        "my custom module name": "foo.bar.baz.qux"
+      },
+      "exactGlobals": true
+    }]
+  ],
+  "moduleId": "my custom module name"
+}
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global/actual.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global/actual.js
new file mode 100644
index 0000000000..7a4e8a723a
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global/actual.js
@@ -0,0 +1 @@
+export default 42;
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global/expected.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global/expected.js
new file mode 100644
index 0000000000..88c2787a3a
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global/expected.js
@@ -0,0 +1,20 @@
+(function (global, factory) {
+  if (typeof define === "function" && define.amd) {
+    define("my custom module name", ["exports"], factory);
+  } else if (typeof exports !== "undefined") {
+    factory(exports);
+  } else {
+    var mod = {
+      exports: {}
+    };
+    factory(mod.exports);
+    global.baz = mod.exports;
+  }
+})(this, function (exports) {
+  "use strict";
+
+  Object.defineProperty(exports, "__esModule", {
+    value: true
+  });
+  exports.default = 42;
+});
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global/options.json b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global/options.json
new file mode 100644
index 0000000000..88df10bb74
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-id-with-overridden-global/options.json
@@ -0,0 +1,12 @@
+{
+  "plugins": [
+    "external-helpers",
+    ["transform-es2015-modules-umd", {
+      "globals": {
+        "my custom module name": "baz"
+      },
+      "exactGlobals": true
+    }]
+  ],
+  "moduleId": "my custom module name"
+}
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-name-with-overridden-global/actual.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-name-with-overridden-global/actual.js
new file mode 100644
index 0000000000..7a4e8a723a
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-name-with-overridden-global/actual.js
@@ -0,0 +1 @@
+export default 42;
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-name-with-overridden-global/expected.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-name-with-overridden-global/expected.js
new file mode 100644
index 0000000000..777602f707
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-name-with-overridden-global/expected.js
@@ -0,0 +1,20 @@
+(function (global, factory) {
+  if (typeof define === "function" && define.amd) {
+    define("umd/module-name-with-overridden-global/expected", ["exports"], factory);
+  } else if (typeof exports !== "undefined") {
+    factory(exports);
+  } else {
+    var mod = {
+      exports: {}
+    };
+    factory(mod.exports);
+    global.baz = mod.exports;
+  }
+})(this, function (exports) {
+  "use strict";
+
+  Object.defineProperty(exports, "__esModule", {
+    value: true
+  });
+  exports.default = 42;
+});
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-name-with-overridden-global/options.json b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-name-with-overridden-global/options.json
new file mode 100644
index 0000000000..8546968383
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/module-name-with-overridden-global/options.json
@@ -0,0 +1,12 @@
+{
+  "plugins": [
+    "external-helpers",
+    ["transform-es2015-modules-umd", {
+      "globals": {
+        "umd/module-name-with-overridden-global/expected": "baz"
+      },
+      "exactGlobals": true
+    }]
+  ],
+  "moduleIds": true
+}
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/override-export-name/actual.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/override-export-name/actual.js
new file mode 100644
index 0000000000..7a4e8a723a
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/override-export-name/actual.js
@@ -0,0 +1 @@
+export default 42;
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/override-export-name/expected.js b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/override-export-name/expected.js
new file mode 100644
index 0000000000..27f66b3fc5
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/override-export-name/expected.js
@@ -0,0 +1,20 @@
+(function (global, factory) {
+  if (typeof define === "function" && define.amd) {
+    define(["exports"], factory);
+  } else if (typeof exports !== "undefined") {
+    factory(exports);
+  } else {
+    var mod = {
+      exports: {}
+    };
+    factory(mod.exports);
+    global.baz = mod.exports;
+  }
+})(this, function (exports) {
+  "use strict";
+
+  Object.defineProperty(exports, "__esModule", {
+    value: true
+  });
+  exports.default = 42;
+});
diff --git a/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/override-export-name/options.json b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/override-export-name/options.json
new file mode 100644
index 0000000000..efdc92bc73
--- /dev/null
+++ b/packages/babel-plugin-transform-es2015-modules-umd/test/fixtures/umd/override-export-name/options.json
@@ -0,0 +1,11 @@
+{
+  "plugins": [
+    "external-helpers",
+    ["transform-es2015-modules-umd", {
+      "globals": {
+        "actual": "baz"
+      },
+      "exactGlobals": true
+    }]
+  ]
+}