diff --git a/llvm/lib/Transforms/IPO/GlobalOpt.cpp b/llvm/lib/Transforms/IPO/GlobalOpt.cpp
--- a/llvm/lib/Transforms/IPO/GlobalOpt.cpp
+++ b/llvm/lib/Transforms/IPO/GlobalOpt.cpp
@@ -2496,10 +2496,19 @@
     // We can't trivially replace the alias with the aliasee if the aliasee is
     // non-trivial in some way. We also can't replace the alias with the aliasee
     // if the aliasee is interposable because aliases point to the local
-    // definition.
+    // definition. On ELF, a non-preemptible alias can be used to access the
+    // definition as if interposition did not happen. This can be the only
+    // approach when using a PC-relative relocation.
     // TODO: Try to handle non-zero GEPs of local aliasees.
     if (!Target || Target->isInterposable())
       continue;
+    const bool JMaybePreemptible =
+        !J->hasLocalLinkage() && J->hasDefaultVisibility();
+    const bool TargetMaybePreemptible =
+        !Target->hasLocalLinkage() && Target->hasDefaultVisibility();
+    if (!JMaybePreemptible && TargetMaybePreemptible)
+      continue;
+
     Target->removeDeadConstantUsers();
 
     // Make all users of the alias use the aliasee instead.
diff --git a/llvm/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll b/llvm/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll
--- a/llvm/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll
+++ b/llvm/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll
@@ -8,7 +8,7 @@
 
 @a = alias void (), void ()* @f
 
-define void @g() {
+define hidden void @g() {
 	call void() @a()
 	ret void
 }
diff --git a/llvm/test/Transforms/GlobalOpt/alias-resolve.ll b/llvm/test/Transforms/GlobalOpt/alias-resolve.ll
--- a/llvm/test/Transforms/GlobalOpt/alias-resolve.ll
+++ b/llvm/test/Transforms/GlobalOpt/alias-resolve.ll
@@ -16,8 +16,13 @@
 @foo4 = weak_odr unnamed_addr alias i8*, getelementptr inbounds ([2 x i8*], [2 x i8*]* @bar4, i32 0, i32 1)
 ; CHECK: @foo4 = weak_odr unnamed_addr alias i8*, getelementptr inbounds ([2 x i8*], [2 x i8*]* @bar4, i32 0, i32 1)
 
-@priva  = private alias void (), void ()* @bar5
-; CHECK: @priva = private alias void (), void ()* @bar5
+@priva1  = private alias void (), void ()* @bar2
+; CHECK: @priva1 = private alias void (), void ()* @bar2
+
+@priva2  = private alias void (), void ()* @bar5
+; CHECK: @priva2 = private alias void (), void ()* @bar5
+
+@priva3  = private alias void (), void ()* @bar6
 
 define void @bar2() {
   ret void
@@ -43,8 +48,14 @@
          call void @weak1()
 ; CHECK: call void @weak1()
 
-         call void @priva()
-; CHECK: call void @priva()
+         call void @priva1()
+; CHECK: call void @priva1()
+
+         call void @priva2()
+; CHECK: call void @priva2()
+
+         call void @priva3()
+; CHECK: call void @bar6()
 
          ret void
 }
@@ -56,3 +67,7 @@
   ret void
 }
 ;CHECK: define void @foo3
+
+define hidden void @bar6() {
+  ret void
+}
diff --git a/llvm/test/Transforms/GlobalOpt/alias-used-address-space.ll b/llvm/test/Transforms/GlobalOpt/alias-used-address-space.ll
--- a/llvm/test/Transforms/GlobalOpt/alias-used-address-space.ll
+++ b/llvm/test/Transforms/GlobalOpt/alias-used-address-space.ll
@@ -2,7 +2,7 @@
 
 target datalayout = "p:32:32:32-p1:16:16:16"
 
-@c = addrspace(1) global i8 42
+@c = hidden addrspace(1) global i8 42
 
 @i = internal addrspace(1) global i8 42
 
diff --git a/llvm/test/Transforms/GlobalOpt/alias-used.ll b/llvm/test/Transforms/GlobalOpt/alias-used.ll
--- a/llvm/test/Transforms/GlobalOpt/alias-used.ll
+++ b/llvm/test/Transforms/GlobalOpt/alias-used.ll
@@ -1,6 +1,6 @@
 ; RUN: opt < %s -globalopt -S | FileCheck %s
 
-@c = global i8 42
+@c = hidden global i8 42
 
 @i = internal global i8 42
 ; CHECK: @ia = internal global i8 42
@@ -30,7 +30,7 @@
 @ca = internal alias i8, i8* @c
 ; CHECK: @ca = internal alias i8, i8* @c
 
-define void @f() {
+define hidden void @f() {
   ret void
 }