diff --git a/packages/babel-plugin-transform-regenerator/src/visit.js b/packages/babel-plugin-transform-regenerator/src/visit.js
index 9750fdd837..15e522ace1 100644
--- a/packages/babel-plugin-transform-regenerator/src/visit.js
+++ b/packages/babel-plugin-transform-regenerator/src/visit.js
@@ -141,6 +141,12 @@ function getOuterFnExpr(funPath) {
   let node = funPath.node;
   t.assertFunction(node);
 
+  if (!node.id){
+    // Default-exported function declarations, and function expressions may not
+    // have a name to reference, so we explicitly add one.
+    node.id = funPath.scope.parent.generateUidIdentifier("callee");
+  }
+
   if (node.generator && // Non-generator functions don't need to be marked.
       t.isFunctionDeclaration(node)) {
     let pp = funPath.findParent(function (path) {
@@ -166,9 +172,7 @@ function getOuterFnExpr(funPath) {
     );
   }
 
-  return node.id || (
-    node.id = funPath.scope.parent.generateUidIdentifier("callee")
-  );
+  return node.id;
 }
 
 function getRuntimeMarkDecl(blockPath) {
diff --git a/packages/babel-plugin-transform-regenerator/test/fixtures/regression/6733/actual.js b/packages/babel-plugin-transform-regenerator/test/fixtures/regression/6733/actual.js
new file mode 100644
index 0000000000..d1201221a7
--- /dev/null
+++ b/packages/babel-plugin-transform-regenerator/test/fixtures/regression/6733/actual.js
@@ -0,0 +1,4 @@
+export default function * () {
+  var x = yield 5;
+  return 5;
+}
diff --git a/packages/babel-plugin-transform-regenerator/test/fixtures/regression/6733/expected.js b/packages/babel-plugin-transform-regenerator/test/fixtures/regression/6733/expected.js
new file mode 100644
index 0000000000..34342c568b
--- /dev/null
+++ b/packages/babel-plugin-transform-regenerator/test/fixtures/regression/6733/expected.js
@@ -0,0 +1,27 @@
+"use strict";
+
+Object.defineProperty(exports, "__esModule", {
+  value: true
+});
+exports.default = _callee;
+
+var _marked = [_callee].map(regeneratorRuntime.mark);
+
+function _callee() {
+  var x;
+  return regeneratorRuntime.wrap(function _callee$(_context) {
+    while (1) switch (_context.prev = _context.next) {
+      case 0:
+        _context.next = 2;
+        return 5;
+
+      case 2:
+        x = _context.sent;
+        return _context.abrupt("return", 5);
+
+      case 4:
+      case "end":
+        return _context.stop();
+    }
+  }, _marked[0], this);
+}
diff --git a/packages/babel-plugin-transform-regenerator/test/fixtures/regression/options.json b/packages/babel-plugin-transform-regenerator/test/fixtures/regression/options.json
new file mode 100644
index 0000000000..3c078e9f99
--- /dev/null
+++ b/packages/babel-plugin-transform-regenerator/test/fixtures/regression/options.json
@@ -0,0 +1,5 @@
+{
+  "presets": [
+    "es2015"
+  ]
+}