diff --git a/compiler/rustc_codegen_llvm/src/common.rs b/compiler/rustc_codegen_llvm/src/common.rs
index 568fcc3f3cf49..cec2f30956e74 100644
--- a/compiler/rustc_codegen_llvm/src/common.rs
+++ b/compiler/rustc_codegen_llvm/src/common.rs
@@ -255,21 +255,34 @@ impl<'ll, 'tcx> ConstMethods<'tcx> for CodegenCx<'ll, 'tcx> {
                 let (prov, offset) = ptr.into_parts();
                 let (base_addr, base_addr_space) = match self.tcx.global_alloc(prov.alloc_id()) {
                     GlobalAlloc::Memory(alloc) => {
-                        let init = const_alloc_to_llvm(self, alloc);
-                        let alloc = alloc.inner();
-                        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::get_value_name(value).is_empty() {
-                            let hash = self.tcx.with_stable_hashing_context(|mut hcx| {
-                                let mut hasher = StableHasher::new();
-                                alloc.hash_stable(&mut hcx, &mut hasher);
-                                hasher.finish::<Hash128>()
-                            });
-                            llvm::set_value_name(value, format!("alloc_{hash:032x}").as_bytes());
+                        // For ZSTs directly codegen an aligned pointer.
+                        // This avoids generating a zero-sized constant value and actually needing a
+                        // real address at runtime.
+                        if alloc.inner().len() == 0 {
+                            let llval = self.const_usize(alloc.inner().align.bytes());
+                            let llval = unsafe { llvm::LLVMConstIntToPtr(llval, llty) };
+                            (llval, AddressSpace::DATA)
+                        } else {
+                            let init = const_alloc_to_llvm(self, alloc);
+                            let alloc = alloc.inner();
+                            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::get_value_name(value).is_empty()
+                            {
+                                let hash = self.tcx.with_stable_hashing_context(|mut hcx| {
+                                    let mut hasher = StableHasher::new();
+                                    alloc.hash_stable(&mut hcx, &mut hasher);
+                                    hasher.finish::<Hash128>()
+                                });
+                                llvm::set_value_name(
+                                    value,
+                                    format!("alloc_{hash:032x}").as_bytes(),
+                                );
+                            }
+                            (value, AddressSpace::DATA)
                         }
-                        (value, AddressSpace::DATA)
                     }
                     GlobalAlloc::Function(fn_instance) => (
                         self.get_fn_addr(fn_instance.polymorphize(self.tcx)),
diff --git a/tests/ui/consts/zst_no_llvm_alloc.rs b/tests/ui/consts/zst_no_llvm_alloc.rs
index 1622a199a7a40..48ef11e2b58cf 100644
--- a/tests/ui/consts/zst_no_llvm_alloc.rs
+++ b/tests/ui/consts/zst_no_llvm_alloc.rs
@@ -6,16 +6,21 @@ struct Foo;
 static FOO: Foo = Foo;
 
 fn main() {
+    // There's no stable guarantee that these are true.
+    // However, we want them to be true so that our LLVM IR and runtime are a bit faster:
+    // a constant address is cheap and doesn't result in relocations in comparison to a "real"
+    // global somewhere in the data section.
     let x: &'static () = &();
-    assert_ne!(x as *const () as usize, 1);
+    assert_eq!(x as *const () as usize, 1);
     let x: &'static Foo = &Foo;
-    assert_ne!(x as *const Foo as usize, 4);
+    assert_eq!(x as *const Foo as usize, 4);
 
-    // statics must have a unique address
-    assert_ne!(&FOO as *const Foo as usize, 4);
+    // The exact addresses returned by these library functions are not necessarily stable guarantees
+    // but for now we assert that we're still matching.
+    assert_eq!(<Vec<i32>>::new().as_ptr(), <&[i32]>::default().as_ptr());
+    assert_eq!(<Box<[i32]>>::default().as_ptr(), (&[]).as_ptr());
 
-    // FIXME this two tests should be assert_eq!
-    // this stopped working since we are promoting to constants instead of statics
-    assert_ne!(<Vec<i32>>::new().as_ptr(), <&[i32]>::default().as_ptr());
-    assert_ne!(<Box<[i32]>>::default().as_ptr(), (&[]).as_ptr());
+    // statics must have a unique address (see https://github.com/rust-lang/rust/issues/18297, not
+    // clear whether this is a stable guarantee)
+    assert_ne!(&FOO as *const Foo as usize, 4);
 }