diff --git a/src/librustc_codegen_llvm/common.rs b/src/librustc_codegen_llvm/common.rs
index 1d6bfb321598c..d2d8097233a4a 100644
--- a/src/librustc_codegen_llvm/common.rs
+++ b/src/librustc_codegen_llvm/common.rs
@@ -259,11 +259,14 @@ impl ConstMethods<'tcx> for CodegenCx<'ll, 'tcx> {
                 let base_addr = match alloc_kind {
                     Some(GlobalAlloc::Memory(alloc)) => {
                         let init = const_alloc_to_llvm(self, alloc);
-                        if alloc.mutability == Mutability::Mut {
-                            self.static_addr_of_mut(init, alloc.align, None)
-                        } else {
-                            self.static_addr_of(init, alloc.align, None)
+                        let value = match alloc.mutability {
+                            Mutability::Mut => self.static_addr_of_mut(init, alloc.align, None),
+                            _ => self.static_addr_of(init, alloc.align, None),
+                        };
+                        if !self.sess().fewer_names() {
+                            llvm::set_value_name(value, format!("{:?}", ptr.alloc_id).as_bytes());
                         }
+                        value
                     }
                     Some(GlobalAlloc::Function(fn_instance)) => self.get_fn_addr(fn_instance),
                     Some(GlobalAlloc::Static(def_id)) => {
diff --git a/src/test/codegen/consts.rs b/src/test/codegen/consts.rs
index a89ecdfd3a901..e53e75b339bef 100644
--- a/src/test/codegen/consts.rs
+++ b/src/test/codegen/consts.rs
@@ -10,11 +10,11 @@
 // CHECK: @STATIC = {{.*}}, align 4
 
 // This checks the constants from inline_enum_const
-// CHECK: @{{[0-9]+}} = {{.*}}, align 2
+// CHECK: @alloc5 = {{.*}}, align 2
 
 // This checks the constants from {low,high}_align_const, they share the same
 // constant, but the alignment differs, so the higher one should be used
-// CHECK: [[LOW_HIGH:@[0-9]+]] = {{.*}} getelementptr inbounds (<{ [8 x i8] }>, <{ [8 x i8] }>* @2, i32 0, i32 0, i32 0), {{.*}},
+// CHECK: [[LOW_HIGH:@[0-9]+]] = {{.*}} getelementptr inbounds (<{ [8 x i8] }>, <{ [8 x i8] }>* @alloc15, i32 0, i32 0, i32 0), {{.*}}
 
 #[derive(Copy, Clone)]
 // repr(i16) is required for the {low,high}_align_const test
diff --git a/src/test/codegen/remap_path_prefix/main.rs b/src/test/codegen/remap_path_prefix/main.rs
index 52ffb97a5b221..4724dc3c3e593 100644
--- a/src/test/codegen/remap_path_prefix/main.rs
+++ b/src/test/codegen/remap_path_prefix/main.rs
@@ -12,7 +12,7 @@ mod aux_mod;
 include!("aux_mod.rs");
 
 // Here we check that the expansion of the file!() macro is mapped.
-// CHECK: @0 = private unnamed_addr constant <{ [34 x i8] }> <{ [34 x i8] c"/the/src/remap_path_prefix/main.rs" }>, align 1
+// CHECK: @alloc1 = private unnamed_addr constant <{ [34 x i8] }> <{ [34 x i8] c"/the/src/remap_path_prefix/main.rs" }>, align 1
 pub static FILE_PATH: &'static str = file!();
 
 fn main() {