diff --git a/lib/Transforms/IPO/GlobalOpt.cpp b/lib/Transforms/IPO/GlobalOpt.cpp
index 4635d0e61c3..1793bbf48ef 100644
--- a/lib/Transforms/IPO/GlobalOpt.cpp
+++ b/lib/Transforms/IPO/GlobalOpt.cpp
@@ -2493,29 +2493,28 @@ bool GlobalOpt::OptimizeGlobalAliases(Module &M) {
       Changed = true;
     }
 
-    // If the aliasee has internal linkage, give it the name and linkage
-    // of the alias, and delete the alias.  This turns:
-    //   define internal ... @f(...)
-    //   @a = alias ... @f
-    // into:
-    //   define ... @a(...)
-    if (!Target->hasLocalLinkage())
-      continue;
+    // If the alias is externally visible, we may still be able to simplify it.
+    if (!J->hasLocalLinkage()) {
+      // If the aliasee has internal linkage, give it the name and linkage
+      // of the alias, and delete the alias.  This turns:
+      //   define internal ... @f(...)
+      //   @a = alias ... @f
+      // into:
+      //   define ... @a(...)
+      if (!Target->hasLocalLinkage())
+        continue;
 
-    // The transform is only useful if the alias does not have internal linkage.
-    if (J->hasLocalLinkage())
-      continue;
+      // Do not perform the transform if multiple aliases potentially target the
+      // aliasee.  This check also ensures that it is safe to replace the section
+      // and other attributes of the aliasee with those of the alias.
+      if (!hasOneUse)
+        continue;
 
-    // Do not perform the transform if multiple aliases potentially target the
-    // aliasee.  This check also ensures that it is safe to replace the section
-    // and other attributes of the aliasee with those of the alias.
-    if (!hasOneUse)
-      continue;
-
-    // Give the aliasee the name, linkage and other attributes of the alias.
-    Target->takeName(J);
-    Target->setLinkage(J->getLinkage());
-    Target->GlobalValue::copyAttributesFrom(J);
+      // Give the aliasee the name, linkage and other attributes of the alias.
+      Target->takeName(J);
+      Target->setLinkage(J->getLinkage());
+      Target->GlobalValue::copyAttributesFrom(J);
+    }
 
     // Delete the alias.
     M.getAliasList().erase(J);
diff --git a/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll b/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll
index 5e639fd8222..a5be2b17d4a 100644
--- a/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll
+++ b/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll
@@ -1,6 +1,8 @@
-; RUN: opt < %s -globalopt -S | grep {define void @a}
+; RUN: opt < %s -globalopt -S | FileCheck %s
 
 define internal void @f() {
+; CHECK-NOT: @f
+; CHECK: define void @a
 	ret void
 }
 
@@ -10,3 +12,13 @@ define void @g() {
 	call void()* @a()
 	ret void
 }
+
+@b = alias internal void ()* @g
+; CHECK-NOT: @b
+
+define void @h() {
+	call void()* @b()
+; CHECK: call void @g
+	ret void
+}
+