diff --git a/lib/compress.js b/lib/compress.js
index 0d6aae80..6f80b25e 100644
--- a/lib/compress.js
+++ b/lib/compress.js
@@ -2021,7 +2021,7 @@ merge(Compressor.prototype, {
         var tw = new TreeWalker(function(node, descend){
             if (node !== self) {
                 if (node instanceof AST_Defun || node instanceof AST_DefClass) {
-                    if (!drop_funcs && scope === self) {
+                    if ((!drop_funcs || tw.parent() instanceof AST_Export) && scope === self) {
                         var node_def = node.name.definition();
                         if (node_def.global && !(node_def.id in in_use_ids)) {
                             in_use_ids[node_def.id] = true;
diff --git a/test/compress/issue-2001.js b/test/compress/issue-2001.js
index 90493aed..80037b91 100644
--- a/test/compress/issue-2001.js
+++ b/test/compress/issue-2001.js
@@ -133,3 +133,35 @@ export_mangle_6: {
     }
     expect_exact: "export let foo=1;"
 }
+
+export_toplevel_1: {
+    options = {
+        toplevel: true,
+        unused: true,
+    }
+    input: {
+        function f(){}
+        export function g(){};
+        export default function h(){};
+    }
+    expect: {
+        export function g(){};
+        export default function(){};
+    }
+}
+
+export_toplevel_2: {
+    options = {
+        toplevel: true,
+        unused: true,
+    }
+    input: {
+        class A {}
+        export class B {};
+        export default class C {};
+    }
+    expect: {
+        export class B {};
+        export default class C {};
+    }
+}