diff --git a/src/Bundle.js b/src/Bundle.js
index b0ef4ac..dcddf13 100644
--- a/src/Bundle.js
+++ b/src/Bundle.js
@@ -10,6 +10,7 @@ import { load, makeOnwarn, resolveId } from './utils/defaults.js';
 import getExportMode from './utils/getExportMode.js';
 import getIndentString from './utils/getIndentString.js';
 import { unixizePath } from './utils/normalizePlatform.js';
+import { mapSequence } from './utils/promise.js';
 import transform from './utils/transform.js';
 import transformBundle from './utils/transformBundle.js';
 import collapseSourcemaps from './utils/collapseSourcemaps.js';
@@ -175,7 +176,7 @@ export default class Bundle {
 	}
 
 	fetchAllDependencies ( module ) {
-		const promises = module.sources.map( source => {
+		return mapSequence( module.sources, source => {
 			return this.resolveId( source, module.id )
 				.then( resolvedId => {
 					// If the `resolvedId` is supposed to be external, make it so.
@@ -205,8 +206,6 @@ export default class Bundle {
 					}
 				});
 		});
-
-		return Promise.all( promises );
 	}
 
 	render ( options = {} ) {
diff --git a/src/utils/promise.js b/src/utils/promise.js
new file mode 100644
index 0000000..1730de8
--- /dev/null
+++ b/src/utils/promise.js
@@ -0,0 +1,16 @@
+import Promise from 'es6-promise/lib/es6-promise/promise.js';
+
+export function mapSequence ( array, fn ) {
+	let results = [];
+	let promise = Promise.resolve();
+
+	function next ( member, i ) {
+		return fn( member ).then( value => results[i] = value );
+	}
+
+	for ( let i = 0; i < array.length; i += 1 ) {
+		promise = promise.then( () => next( array[i], i ) );
+	}
+
+	return promise.then( () => results );
+}