diff --git a/compiler/rustc_const_eval/src/interpret/memory.rs b/compiler/rustc_const_eval/src/interpret/memory.rs
index 0790db984e345..2772c94d52b0b 100644
--- a/compiler/rustc_const_eval/src/interpret/memory.rs
+++ b/compiler/rustc_const_eval/src/interpret/memory.rs
@@ -1481,22 +1481,31 @@ impl<'tcx, M: Machine<'tcx>> InterpCx<'tcx, M> {
     /// Test if this value might be null.
     /// If the machine does not support ptr-to-int casts, this is conservative.
     pub fn scalar_may_be_null(&self, scalar: Scalar<M::Provenance>) -> InterpResult<'tcx, bool> {
-        interp_ok(match scalar.try_to_scalar_int() {
-            Ok(int) => int.is_null(),
+        match scalar.try_to_scalar_int() {
+            Ok(int) => interp_ok(int.is_null()),
             Err(_) => {
-                // Can only happen during CTFE.
+                // We can't cast this pointer to an integer. Can only happen during CTFE.
                 let ptr = scalar.to_pointer(self)?;
                 match self.ptr_try_get_alloc_id(ptr, 0) {
                     Ok((alloc_id, offset, _)) => {
-                        let size = self.get_alloc_info(alloc_id).size;
-                        // If the pointer is out-of-bounds, it may be null.
-                        // Note that one-past-the-end (offset == size) is still inbounds, and never null.
-                        offset > size
+                        let info = self.get_alloc_info(alloc_id);
+                        // If the pointer is in-bounds (including "at the end"), it is definitely not null.
+                        if offset <= info.size {
+                            return interp_ok(false);
+                        }
+                        // If the allocation is N-aligned, and the offset is not divisible by N,
+                        // then `base + offset` has a non-zero remainder after division by `N`,
+                        // which means `base + offset` cannot be null.
+                        if offset.bytes() % info.align.bytes() != 0 {
+                            return interp_ok(false);
+                        }
+                        // We don't know enough, this might be null.
+                        interp_ok(true)
                     }
                     Err(_offset) => bug!("a non-int scalar is always a pointer"),
                 }
             }
-        })
+        }
     }
 
     /// Turning a "maybe pointer" into a proper pointer (and some information
diff --git a/tests/ui/consts/const-ptr-is-null.rs b/tests/ui/consts/const-ptr-is-null.rs
index 92cf87a9782f2..0abd9afa42246 100644
--- a/tests/ui/consts/const-ptr-is-null.rs
+++ b/tests/ui/consts/const-ptr-is-null.rs
@@ -12,7 +12,13 @@ const MAYBE_NULL: () = {
     let ptr = &x as *const i32;
     // This one is still unambiguous...
     assert!(!ptr.is_null());
-    // but once we shift outside the allocation, we might become null.
+    // and in fact, any offset not visible by 4 (the alignment) cannot be null,
+    // even if it goes out-of-bounds...
+    assert!(!ptr.wrapping_byte_add(13).is_null());
+    assert!(!ptr.wrapping_byte_add(18).is_null());
+    assert!(!ptr.wrapping_byte_sub(1).is_null());
+    // ... but once we shift outside the allocation, with an offset divisible by 4,
+    // we might become null.
     assert!(!ptr.wrapping_sub(512).is_null()); //~inside `MAYBE_NULL`
 };
 
diff --git a/tests/ui/consts/const-ptr-is-null.stderr b/tests/ui/consts/const-ptr-is-null.stderr
index f71b37527726f..5ef79790d93bc 100644
--- a/tests/ui/consts/const-ptr-is-null.stderr
+++ b/tests/ui/consts/const-ptr-is-null.stderr
@@ -8,7 +8,7 @@ note: inside `std::ptr::const_ptr::<impl *const T>::is_null::compiletime`
 note: inside `std::ptr::const_ptr::<impl *const i32>::is_null`
   --> $SRC_DIR/core/src/ptr/const_ptr.rs:LL:COL
 note: inside `MAYBE_NULL`
-  --> $DIR/const-ptr-is-null.rs:16:14
+  --> $DIR/const-ptr-is-null.rs:22:14
    |
 LL |     assert!(!ptr.wrapping_sub(512).is_null());
    |              ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^