diff --git a/compiler/rustc_typeck/src/check/dropck.rs b/compiler/rustc_typeck/src/check/dropck.rs
index 3cc66aaf0d79..919524017aad 100644
--- a/compiler/rustc_typeck/src/check/dropck.rs
+++ b/compiler/rustc_typeck/src/check/dropck.rs
@@ -230,9 +230,15 @@ fn ensure_drop_predicates_are_implied_by_item_defn<'tcx>(
             let predicate = predicate.kind();
             let p = p.kind();
             match (predicate.skip_binder(), p.skip_binder()) {
-                (ty::PredicateKind::Trait(a), ty::PredicateKind::Trait(b)) => {
-                    relator.relate(predicate.rebind(a), p.rebind(b)).is_ok()
-                }
+                (ty::PredicateKind::Trait(a), ty::PredicateKind::Trait(b)) => relator
+                    .relate(
+                        predicate.rebind(ty::TraitPredicate {
+                            constness: ty::BoundConstness::NotConst,
+                            ..a
+                        }),
+                        p.rebind(b),
+                    )
+                    .is_ok(),
                 (ty::PredicateKind::Projection(a), ty::PredicateKind::Projection(b)) => {
                     relator.relate(predicate.rebind(a), p.rebind(b)).is_ok()
                 }
diff --git a/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.precise.stderr b/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.precise.stderr
index 04c21101e758..3fb59a4e0057 100644
--- a/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.precise.stderr
+++ b/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.precise.stderr
@@ -1,11 +1,3 @@
-error: `~const` is not allowed here
-  --> $DIR/const-drop-fail.rs:27:35
-   |
-LL | struct ConstDropImplWithBounds<T: ~const A>(PhantomData<T>);
-   |                                   ^^^^^^^^
-   |
-   = note: only allowed on bounds on traits' associated types and functions, const fns, const impls and its associated functions
-
 error[E0277]: the trait bound `NonTrivialDrop: Drop` is not satisfied
   --> $DIR/const-drop-fail.rs:45:5
    |
diff --git a/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.rs b/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.rs
index 3d4de088f553..fd7271563d12 100644
--- a/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.rs
+++ b/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.rs
@@ -24,8 +24,7 @@ trait A { fn a() { println!("A"); } }
 
 impl A for NonTrivialDrop {}
 
-struct ConstDropImplWithBounds<T: ~const A>(PhantomData<T>);
-//~^ ERROR `~const` is not allowed
+struct ConstDropImplWithBounds<T: A>(PhantomData<T>);
 
 impl<T: ~const A> const Drop for ConstDropImplWithBounds<T> {
     fn drop(&mut self) {
diff --git a/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.stock.stderr b/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.stock.stderr
index 04c21101e758..3fb59a4e0057 100644
--- a/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.stock.stderr
+++ b/src/test/ui/rfc-2632-const-trait-impl/const-drop-fail.stock.stderr
@@ -1,11 +1,3 @@
-error: `~const` is not allowed here
-  --> $DIR/const-drop-fail.rs:27:35
-   |
-LL | struct ConstDropImplWithBounds<T: ~const A>(PhantomData<T>);
-   |                                   ^^^^^^^^
-   |
-   = note: only allowed on bounds on traits' associated types and functions, const fns, const impls and its associated functions
-
 error[E0277]: the trait bound `NonTrivialDrop: Drop` is not satisfied
   --> $DIR/const-drop-fail.rs:45:5
    |
diff --git a/src/test/ui/rfc-2632-const-trait-impl/const-drop.rs b/src/test/ui/rfc-2632-const-trait-impl/const-drop.rs
index 292017a1de24..e1b3bc12706c 100644
--- a/src/test/ui/rfc-2632-const-trait-impl/const-drop.rs
+++ b/src/test/ui/rfc-2632-const-trait-impl/const-drop.rs
@@ -45,6 +45,15 @@ mod t {
 
     pub struct HasConstDrop(pub ConstDrop);
     pub struct TrivialFields(pub u8, pub i8, pub usize, pub isize);
+
+    pub trait SomeTrait {}
+    impl const SomeTrait for () {}
+
+    pub struct ConstDropWithBound<T: SomeTrait>;
+
+    impl<T: ~const SomeTrait> const Drop for ConstDropWithBound<T> {
+        fn drop(&mut self) {}
+    }
 }
 
 use t::*;
@@ -61,6 +70,7 @@ implements_const_drop! {
     TrivialFields(1, 2, 3, 4),
     &1,
     &1 as *const i32,
+    ConstDropWithBound<()>,
 }
 
 fn main() {