diff --git a/lib/compress.js b/lib/compress.js
index 9f17efb5..d6a1830a 100644
--- a/lib/compress.js
+++ b/lib/compress.js
@@ -2226,9 +2226,7 @@ merge(Compressor.prototype, {
             function before(node, descend, in_list) {
                 var parent = tt.parent();
                 if (!compressor.option("keep_fnames")
-                    && ((node instanceof AST_Function || node instanceof AST_ClassExpression) && node.name
-                        || (node instanceof AST_Defun || node instanceof AST_DefClass)
-                            && parent instanceof AST_Export && parent.is_default)) {
+                    && node.name && (node instanceof AST_Function || node instanceof AST_ClassExpression)) {
                     var def = node.name.definition();
                     // any declarations with same name will overshadow
                     // name of this anonymous function and can therefore
diff --git a/test/compress/harmony.js b/test/compress/harmony.js
index 95ba07eb..45459eee 100644
--- a/test/compress/harmony.js
+++ b/test/compress/harmony.js
@@ -664,3 +664,31 @@ class_expression_statement_unused_toplevel: {
     }
     expect_exact: ""
 }
+
+export_default_function_decl: {
+    options = {
+        toplevel: true,
+        passes: 3,
+        unused: true,
+    }
+    input: {
+        // do not drop "unused" exports
+        export default function Foo() {};
+        export function Far() {};
+    }
+    expect_exact: "export default function Foo(){};export function Far(){};"
+}
+
+export_default_class_decl: {
+    options = {
+        toplevel: true,
+        passes: 3,
+        unused: true,
+    }
+    input: {
+        // do not drop "unused" exports
+        export default class Car {};
+        export class Cab {};
+    }
+    expect_exact: "export default class Car{};export class Cab{};"
+}
diff --git a/test/compress/issue-2001.js b/test/compress/issue-2001.js
index 0109641b..a4e779ea 100644
--- a/test/compress/issue-2001.js
+++ b/test/compress/issue-2001.js
@@ -45,7 +45,7 @@ export_default_func_1: {
     input: {
         export default function f(){};
     }
-    expect_exact: "export default function(){};"
+    expect_exact: "export default function f(){};"
 }
 
 export_default_func_2: {
@@ -58,7 +58,7 @@ export_default_func_2: {
     input: {
         export default function f(){}(1);
     }
-    expect_exact: "export default function(){};1;"
+    expect_exact: "export default function f(){};1;"
 }
 
 export_default_func_3: {
@@ -71,7 +71,7 @@ export_default_func_3: {
     input: {
         export default function f(){}(1);
     }
-    expect_exact: "export default function(){};"
+    expect_exact: "export default function f(){};"
 }
 
 export_class_1: {
@@ -121,7 +121,7 @@ export_default_class_1: {
     input: {
         export default class C {};
     }
-    expect_exact: "export default class{};"
+    expect_exact: "export default class C{};"
 }
 
 export_default_class_2: {
@@ -134,7 +134,7 @@ export_default_class_2: {
     input: {
         export default class C {}(1);
     }
-    expect_exact: "export default class{};1;"
+    expect_exact: "export default class C{};1;"
 }
 
 export_default_class_3: {
@@ -147,7 +147,7 @@ export_default_class_3: {
     input: {
         export default class C {}(1);
     }
-    expect_exact: "export default class{};"
+    expect_exact: "export default class C{};"
 }
 
 export_mangle_1: {
@@ -247,7 +247,7 @@ export_toplevel_1: {
     }
     expect: {
         export function g(){};
-        export default function(){};
+        export default function h(){};
     }
 }
 
@@ -263,7 +263,7 @@ export_toplevel_2: {
     }
     expect: {
         export class B {};
-        export default class {};
+        export default class C {};
     }
 }