diff --git a/packages/babel-generator/src/node/parentheses.js b/packages/babel-generator/src/node/parentheses.js
index b511d471f7..cb7642c7a1 100644
--- a/packages/babel-generator/src/node/parentheses.js
+++ b/packages/babel-generator/src/node/parentheses.js
@@ -121,7 +121,15 @@ export function YieldExpression(node, parent) {
 }
 
 export function ClassExpression(node, parent) {
-  return t.isExpressionStatement(parent);
+  // (class {});
+  if (t.isExpressionStatement(parent)) {
+    return true;
+  }
+
+  // export default (class () {});
+  if (t.isExportDeclaration(parent)) {
+    return true;
+  }
 }
 
 export function UnaryLike(node, parent) {
@@ -129,11 +137,16 @@ export function UnaryLike(node, parent) {
 }
 
 export function FunctionExpression(node, parent) {
-  // function () {};
+  // (function () {});
   if (t.isExpressionStatement(parent)) {
     return true;
   }
 
+  // export default (function () {});
+  if (t.isExportDeclaration(parent)) {
+    return true;
+  }
+
   // (function test() {}).name;
   if (t.isMemberExpression(parent) && parent.object === node) {
     return true;
diff --git a/packages/babylon/src/parser/statement.js b/packages/babylon/src/parser/statement.js
index 1d8ea87793..614951c802 100644
--- a/packages/babylon/src/parser/statement.js
+++ b/packages/babylon/src/parser/statement.js
@@ -673,10 +673,8 @@ pp.parseExport = function (node) {
     let needsSemi = false;
     if (this.eat(tt._function)) {
       expr = this.parseFunction(expr, true, false, false, true);
-      if (!expr.id) expr.type = "FunctionExpression";
     } else if (this.match(tt._class)) {
       expr = this.parseClass(expr, true, true);
-      if (!expr.id) expr.type = "ClassExpression";
     } else {
       needsSemi = true;
       expr = this.parseMaybeAssign();