diff --git a/packages/babel-preset-react-app/index.js b/packages/babel-preset-react-app/index.js
index d3063aee304..d6e9c4519d4 100644
--- a/packages/babel-preset-react-app/index.js
+++ b/packages/babel-preset-react-app/index.js
@@ -27,7 +27,15 @@ const plugins = [
       regenerator: true,
       // Resolve the Babel runtime relative to the config.
       moduleName: path.dirname(require.resolve('babel-runtime/package'))
-    }]
+    }],
+    // The following two plugins are currently necessary to get
+    // babel-preset-env to work with rest/spread. More info here:
+    // https://github.com/babel/babel-preset-env#caveats
+    // https://github.com/babel/babel/issues/4074
+    // const { a, ...z } = obj;
+    require.resolve('babel-plugin-transform-es2015-destructuring'),
+    // const fn = ({ a, ...otherProps }) => otherProps;
+    require.resolve('babel-plugin-transform-es2015-parameters')
   ];
 
 // This is similar to how `env` works in Babel:
diff --git a/packages/babel-preset-react-app/package.json b/packages/babel-preset-react-app/package.json
index bd1db0f5722..3778880b5ce 100644
--- a/packages/babel-preset-react-app/package.json
+++ b/packages/babel-preset-react-app/package.json
@@ -12,6 +12,8 @@
   ],
   "dependencies": {
     "babel-plugin-transform-class-properties": "6.11.5",
+    "babel-plugin-transform-es2015-destructuring": "6.16.0",
+    "babel-plugin-transform-es2015-parameters": "6.17.0",
     "babel-plugin-transform-object-rest-spread": "6.8.0",
     "babel-plugin-transform-react-constant-elements": "6.9.1",
     "babel-plugin-transform-react-jsx-self": "6.11.0",