diff --git a/compiler/rustc_hir_analysis/src/check/dropck.rs b/compiler/rustc_hir_analysis/src/check/dropck.rs
index e5b212eb757b..3d55ffc595f5 100644
--- a/compiler/rustc_hir_analysis/src/check/dropck.rs
+++ b/compiler/rustc_hir_analysis/src/check/dropck.rs
@@ -184,13 +184,7 @@ fn ensure_drop_predicates_are_implied_by_item_defn<'tcx>(
             let p = p.kind();
             match (predicate.skip_binder(), p.skip_binder()) {
                 (ty::PredicateKind::Trait(a), ty::PredicateKind::Trait(b)) => {
-                    // Since struct predicates cannot have ~const, project the impl predicate
-                    // onto one that ignores the constness. This is equivalent to saying that
-                    // we match a `Trait` bound on the struct with a `Trait` or `~const Trait`
-                    // in the impl.
-                    let non_const_a =
-                        ty::TraitPredicate { constness: ty::BoundConstness::NotConst, ..a };
-                    relator.relate(predicate.rebind(non_const_a), p.rebind(b)).is_ok()
+                    relator.relate(predicate.rebind(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 ddf0e2d91c09..796c0d388eaf 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
@@ -45,34 +45,55 @@ note: required by a bound in `check`
 LL | const fn check<T: ~const Destruct>(_: T) {}
    |                   ^^^^^^^^^^^^^^^ required by this bound in `check`
 
-error[E0277]: the trait bound `ConstDropImplWithBounds<NonTrivialDrop>: ~const Destruct` is not satisfied
+error[E0277]: the trait bound `NonTrivialDrop: ~const A` is not satisfied
+  --> $DIR/const-drop-fail.rs:48:47
+   |
+LL |     ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
+   |     ----------------------------------------- ^^^^^^^^^^^ the trait `~const A` is not implemented for `NonTrivialDrop`
+   |     |
+   |     required by a bound introduced by this call
+   |
+note: the trait `A` is implemented for `NonTrivialDrop`, but that implementation is not `const`
+  --> $DIR/const-drop-fail.rs:48:47
+   |
+LL |     ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
+   |                                               ^^^^^^^^^^^
+note: required by a bound in `ConstDropImplWithBounds`
+  --> $DIR/const-drop-fail.rs:27:35
+   |
+LL | struct ConstDropImplWithBounds<T: ~const A>(PhantomData<T>);
+   |                                   ^^^^^^^^ required by this bound in `ConstDropImplWithBounds`
+
+error[E0277]: the trait bound `NonTrivialDrop: ~const A` is not satisfied
   --> $DIR/const-drop-fail.rs:48:5
    |
-LL |         const _: () = check($exp);
-   |                       ----- required by a bound introduced by this call
-...
 LL |     ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
-   |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ the trait `~const Destruct` is not implemented for `ConstDropImplWithBounds<NonTrivialDrop>`
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ the trait `~const A` is not implemented for `NonTrivialDrop`
    |
-note: required for `ConstDropImplWithBounds<NonTrivialDrop>` to implement `~const Destruct`
-  --> $DIR/const-drop-fail.rs:29:25
+note: the trait `A` is implemented for `NonTrivialDrop`, but that implementation is not `const`
+  --> $DIR/const-drop-fail.rs:48:5
    |
-LL | impl<T: ~const A> const Drop for ConstDropImplWithBounds<T> {
-   |                         ^^^^     ^^^^^^^^^^^^^^^^^^^^^^^^^^
-   = note: 1 redundant requirement hidden
-   = note: required for `ConstDropImplWithBounds<NonTrivialDrop>` to implement `~const Destruct`
-note: required by a bound in `check`
-  --> $DIR/const-drop-fail.rs:35:19
+LL |     ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+note: required by a bound in `ConstDropImplWithBounds`
+  --> $DIR/const-drop-fail.rs:27:35
    |
-LL | const fn check<T: ~const Destruct>(_: T) {}
-   |                   ^^^^^^^^^^^^^^^ required by this bound in `check`
-help: consider borrowing here
-   |
-LL |     &ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
-   |     +
-LL |     &mut ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
-   |     ++++
+LL | struct ConstDropImplWithBounds<T: ~const A>(PhantomData<T>);
+   |                                   ^^^^^^^^ required by this bound in `ConstDropImplWithBounds`
 
-error: aborting due to 3 previous errors
+error[E0367]: `Drop` impl requires `T: ~const A` but the struct it is implemented for does not
+  --> $DIR/const-drop-fail.rs:55:9
+   |
+LL | impl<T: ~const A> const Drop for ConstDropImplWithNonConstBounds<T> {
+   |         ^^^^^^^^
+   |
+note: the implementor must specify the same requirement
+  --> $DIR/const-drop-fail.rs:53:1
+   |
+LL | struct ConstDropImplWithNonConstBounds<T: A>(PhantomData<T>);
+   | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-For more information about this error, try `rustc --explain E0277`.
+error: aborting due to 5 previous errors
+
+Some errors have detailed explanations: E0277, E0367.
+For more information about an error, try `rustc --explain E0277`.
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 565e2c77ac5c..d36c7f81ced8 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
@@ -24,7 +24,7 @@ trait A { fn a() { } }
 
 impl A for NonTrivialDrop {}
 
-struct ConstDropImplWithBounds<T: A>(PhantomData<T>);
+struct ConstDropImplWithBounds<T: ~const A>(PhantomData<T>);
 
 impl<T: ~const A> const Drop for ConstDropImplWithBounds<T> {
     fn drop(&mut self) {
@@ -47,6 +47,16 @@ check_all! {
     //~^ ERROR can't drop
     ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
     //~^ ERROR the trait bound
+    //~| ERROR the trait bound
+}
+
+struct ConstDropImplWithNonConstBounds<T: A>(PhantomData<T>);
+
+impl<T: ~const A> const Drop for ConstDropImplWithNonConstBounds<T> {
+//~^ ERROR `Drop` impl requires `T: ~const A` but the struct it is implemented for does not
+    fn drop(&mut self) {
+        T::a();
+    }
 }
 
 fn main() {}
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 ddf0e2d91c09..796c0d388eaf 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
@@ -45,34 +45,55 @@ note: required by a bound in `check`
 LL | const fn check<T: ~const Destruct>(_: T) {}
    |                   ^^^^^^^^^^^^^^^ required by this bound in `check`
 
-error[E0277]: the trait bound `ConstDropImplWithBounds<NonTrivialDrop>: ~const Destruct` is not satisfied
+error[E0277]: the trait bound `NonTrivialDrop: ~const A` is not satisfied
+  --> $DIR/const-drop-fail.rs:48:47
+   |
+LL |     ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
+   |     ----------------------------------------- ^^^^^^^^^^^ the trait `~const A` is not implemented for `NonTrivialDrop`
+   |     |
+   |     required by a bound introduced by this call
+   |
+note: the trait `A` is implemented for `NonTrivialDrop`, but that implementation is not `const`
+  --> $DIR/const-drop-fail.rs:48:47
+   |
+LL |     ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
+   |                                               ^^^^^^^^^^^
+note: required by a bound in `ConstDropImplWithBounds`
+  --> $DIR/const-drop-fail.rs:27:35
+   |
+LL | struct ConstDropImplWithBounds<T: ~const A>(PhantomData<T>);
+   |                                   ^^^^^^^^ required by this bound in `ConstDropImplWithBounds`
+
+error[E0277]: the trait bound `NonTrivialDrop: ~const A` is not satisfied
   --> $DIR/const-drop-fail.rs:48:5
    |
-LL |         const _: () = check($exp);
-   |                       ----- required by a bound introduced by this call
-...
 LL |     ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
-   |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ the trait `~const Destruct` is not implemented for `ConstDropImplWithBounds<NonTrivialDrop>`
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ the trait `~const A` is not implemented for `NonTrivialDrop`
    |
-note: required for `ConstDropImplWithBounds<NonTrivialDrop>` to implement `~const Destruct`
-  --> $DIR/const-drop-fail.rs:29:25
+note: the trait `A` is implemented for `NonTrivialDrop`, but that implementation is not `const`
+  --> $DIR/const-drop-fail.rs:48:5
    |
-LL | impl<T: ~const A> const Drop for ConstDropImplWithBounds<T> {
-   |                         ^^^^     ^^^^^^^^^^^^^^^^^^^^^^^^^^
-   = note: 1 redundant requirement hidden
-   = note: required for `ConstDropImplWithBounds<NonTrivialDrop>` to implement `~const Destruct`
-note: required by a bound in `check`
-  --> $DIR/const-drop-fail.rs:35:19
+LL |     ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+note: required by a bound in `ConstDropImplWithBounds`
+  --> $DIR/const-drop-fail.rs:27:35
    |
-LL | const fn check<T: ~const Destruct>(_: T) {}
-   |                   ^^^^^^^^^^^^^^^ required by this bound in `check`
-help: consider borrowing here
-   |
-LL |     &ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
-   |     +
-LL |     &mut ConstDropImplWithBounds::<NonTrivialDrop>(PhantomData),
-   |     ++++
+LL | struct ConstDropImplWithBounds<T: ~const A>(PhantomData<T>);
+   |                                   ^^^^^^^^ required by this bound in `ConstDropImplWithBounds`
 
-error: aborting due to 3 previous errors
+error[E0367]: `Drop` impl requires `T: ~const A` but the struct it is implemented for does not
+  --> $DIR/const-drop-fail.rs:55:9
+   |
+LL | impl<T: ~const A> const Drop for ConstDropImplWithNonConstBounds<T> {
+   |         ^^^^^^^^
+   |
+note: the implementor must specify the same requirement
+  --> $DIR/const-drop-fail.rs:53:1
+   |
+LL | struct ConstDropImplWithNonConstBounds<T: A>(PhantomData<T>);
+   | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-For more information about this error, try `rustc --explain E0277`.
+error: aborting due to 5 previous errors
+
+Some errors have detailed explanations: E0277, E0367.
+For more information about an error, try `rustc --explain E0277`.
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 8b4c40658156..b0fc3adf984a 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
@@ -60,7 +60,7 @@ mod t {
         fn foo() {}
     }
 
-    pub struct ConstDropWithBound<T: SomeTrait>(pub core::marker::PhantomData<T>);
+    pub struct ConstDropWithBound<T: ~const SomeTrait>(pub core::marker::PhantomData<T>);
 
     impl<T: ~const SomeTrait> const Drop for ConstDropWithBound<T> {
         fn drop(&mut self) {
diff --git a/src/test/ui/rfc-2632-const-trait-impl/tilde_const_on_impl_bound.rs b/src/test/ui/rfc-2632-const-trait-impl/tilde_const_on_impl_bound.rs
new file mode 100644
index 000000000000..285cef571f33
--- /dev/null
+++ b/src/test/ui/rfc-2632-const-trait-impl/tilde_const_on_impl_bound.rs
@@ -0,0 +1,17 @@
+// check-pass
+#![feature(const_trait_impl)]
+
+#[const_trait]
+trait Foo {
+    fn foo(&self) {}
+}
+
+struct Bar<T>(T);
+
+impl<T: ~const Foo> Bar<T> {
+    const fn foo(&self) {
+        self.0.foo()
+    }
+}
+
+fn main() {}