diff --git a/src/librustc_codegen_llvm/common.rs b/src/librustc_codegen_llvm/common.rs
index b0c94a139be08..19f18088579b3 100644
--- a/src/librustc_codegen_llvm/common.rs
+++ b/src/librustc_codegen_llvm/common.rs
@@ -333,15 +333,21 @@ impl ConstMethods<'tcx> for CodegenCx<'ll, 'tcx> {
         offset: Size,
     ) -> PlaceRef<'tcx, &'ll Value> {
         assert_eq!(alloc.align, layout.align.abi);
-        let init = const_alloc_to_llvm(self, alloc);
-        let base_addr = self.static_addr_of(init, alloc.align, None);
-
-        let llval = unsafe { llvm::LLVMConstInBoundsGEP(
-            self.const_bitcast(base_addr, self.type_i8p()),
-            &self.const_usize(offset.bytes()),
-            1,
-        )};
-        let llval = self.const_bitcast(llval, self.type_ptr_to(layout.llvm_type(self)));
+        let llty = self.type_ptr_to(layout.llvm_type(self));
+        let llval = if layout.size == Size::ZERO {
+            let llval = self.const_usize(alloc.align.bytes());
+            unsafe { llvm::LLVMConstIntToPtr(llval, llty) }
+        } else {
+            let init = const_alloc_to_llvm(self, alloc);
+            let base_addr = self.static_addr_of(init, alloc.align, None);
+
+            let llval = unsafe { llvm::LLVMConstInBoundsGEP(
+                self.const_bitcast(base_addr, self.type_i8p()),
+                &self.const_usize(offset.bytes()),
+                1,
+            )};
+            self.const_bitcast(llval, llty)
+        };
         PlaceRef::new_sized(llval, layout, alloc.align)
     }
 
diff --git a/src/test/ui/consts/zst_no_llvm_alloc.rs b/src/test/ui/consts/zst_no_llvm_alloc.rs
new file mode 100644
index 0000000000000..5d779355400cc
--- /dev/null
+++ b/src/test/ui/consts/zst_no_llvm_alloc.rs
@@ -0,0 +1,19 @@
+// run-pass
+
+#[repr(align(4))]
+struct Foo;
+
+static FOO: Foo = Foo;
+
+fn main() {
+    let x: &'static () = &();
+    assert_eq!(x as *const () as usize, 1);
+    let x: &'static Foo = &Foo;
+    assert_eq!(x as *const Foo as usize, 4);
+
+    // statics must have a unique address
+    assert_ne!(&FOO as *const Foo as usize, 4);
+
+    assert_eq!(<Vec<i32>>::new().as_ptr(), <&[i32]>::default().as_ptr());
+    assert_eq!(<Box<[i32]>>::default().as_ptr(), (&[]).as_ptr());
+}