diff --git a/lib/compress.js b/lib/compress.js
index e3bfa938..4065c543 100644
--- a/lib/compress.js
+++ b/lib/compress.js
@@ -409,7 +409,6 @@ merge(Compressor.prototype, {
                     }
                 }
                 if (node instanceof AST_DefClass || node instanceof AST_Defun) {
-                    if (!node.name) return;
                     node.inlined = false;
                     var d = node.name.definition();
                     if (compressor.exposed(d) || safe_to_read(d)) {
@@ -2582,7 +2581,6 @@ merge(Compressor.prototype, {
             if (node instanceof AST_Defun || node instanceof AST_DefClass) {
                 var in_export = tw.parent() instanceof AST_Export;
                 if (in_export || !drop_funcs && scope === self) {
-                    if (!node.name) return;
                     var node_def = node.name.definition();
                     if (node_def.global && !(node_def.id in in_use_ids)) {
                         in_use_ids[node_def.id] = true;
@@ -2668,7 +2666,6 @@ merge(Compressor.prototype, {
                 if (node.name
                     && (!compressor.option("keep_classnames") && node instanceof AST_ClassExpression
                         || !compressor.option("keep_fnames") && node instanceof AST_Function)) {
-                    if (!node.name) return;
                     var def = node.name.definition();
                     // any declarations with same name will overshadow
                     // name of this anonymous function and can therefore
@@ -2704,7 +2701,6 @@ merge(Compressor.prototype, {
                     }
                 }
                 if ((node instanceof AST_Defun || node instanceof AST_DefClass) && node !== self) {
-                    if (!node.name) return;
                     var def = node.name.definition();
                     var keep = (def.id in in_use_ids) || !drop_funcs && def.global;
                     if (!keep) {
diff --git a/lib/parse.js b/lib/parse.js
index f97a8b2a..eebc4967 100644
--- a/lib/parse.js
+++ b/lib/parse.js
@@ -1310,7 +1310,7 @@ function parse($TEXT, options) {
 
     var function_ = function(ctor, is_generator_property, is_async, is_export_default) {
         if (is_generator_property && is_async) croak("generators cannot be async");
-        var start = S.token
+        var start = S.token;
 
         var in_statement = ctor === AST_Defun;
         var is_generator = is("operator", "*");
@@ -1319,8 +1319,13 @@ function parse($TEXT, options) {
         }
 
         var name = is("name") ? as_symbol(in_statement ? AST_SymbolDefun : AST_SymbolLambda) : null;
-        if (in_statement && !name && !is_export_default)
-            unexpected();
+        if (in_statement && !name) {
+            if (is_export_default) {
+                ctor = AST_Function;
+            } else {
+                unexpected();
+            }
+        }
 
         if (name && ctor !== AST_Accessor && !(name instanceof AST_SymbolDeclaration))
             unexpected(prev());
@@ -2530,7 +2535,7 @@ function parse($TEXT, options) {
             semicolon();
         } else if ((node = statement(is_default)) instanceof AST_Definitions && is_default) {
             unexpected(node.start);
-        } else if (node instanceof AST_Definitions || node instanceof AST_Defun || node instanceof AST_DefClass) {
+        } else if (node instanceof AST_Definitions || node instanceof AST_Lambda || node instanceof AST_DefClass) {
             exported_definition = node;
         } else if (node instanceof AST_SimpleStatement) {
             exported_value = node.body;