diff --git a/compiler/rustc_middle/src/traits/select.rs b/compiler/rustc_middle/src/traits/select.rs
index 53af3e9053419..6bcdfd6394a94 100644
--- a/compiler/rustc_middle/src/traits/select.rs
+++ b/compiler/rustc_middle/src/traits/select.rs
@@ -119,8 +119,9 @@ pub enum SelectionCandidate<'tcx> {
 
     /// This is a trait matching with a projected type as `Self`, and we found
     /// an applicable bound in the trait definition. The `usize` is an index
-    /// into the list returned by `tcx.item_bounds`.
-    ProjectionCandidate(usize),
+    /// into the list returned by `tcx.item_bounds`. The constness is the
+    /// constness of the bound in the trait.
+    ProjectionCandidate(usize, ty::BoundConstness),
 
     /// Implementation of a `Fn`-family trait by one of the anonymous types
     /// generated for an `||` expression.
diff --git a/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs b/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs
index a80527f63a004..451427a69807d 100644
--- a/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs
+++ b/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs
@@ -362,7 +362,9 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
             .infcx
             .probe(|_| self.match_projection_obligation_against_definition_bounds(obligation));
 
-        candidates.vec.extend(result.into_iter().map(ProjectionCandidate));
+        candidates
+            .vec
+            .extend(result.into_iter().map(|(idx, constness)| ProjectionCandidate(idx, constness)));
     }
 
     /// Given an obligation like `<SomeTrait for T>`, searches the obligations that the caller
diff --git a/compiler/rustc_trait_selection/src/traits/select/confirmation.rs b/compiler/rustc_trait_selection/src/traits/select/confirmation.rs
index 8b24e83ffa497..52bc8115fa027 100644
--- a/compiler/rustc_trait_selection/src/traits/select/confirmation.rs
+++ b/compiler/rustc_trait_selection/src/traits/select/confirmation.rs
@@ -68,10 +68,9 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
                 ImplSource::AutoImpl(data)
             }
 
-            ProjectionCandidate(idx) => {
+            ProjectionCandidate(idx, constness) => {
                 let obligations = self.confirm_projection_candidate(obligation, idx)?;
-                // FIXME(jschievink): constness
-                ImplSource::Param(obligations, ty::BoundConstness::NotConst)
+                ImplSource::Param(obligations, constness)
             }
 
             ObjectCandidate(idx) => {
diff --git a/compiler/rustc_trait_selection/src/traits/select/mod.rs b/compiler/rustc_trait_selection/src/traits/select/mod.rs
index cff6b61ee3364..e4e0258456136 100644
--- a/compiler/rustc_trait_selection/src/traits/select/mod.rs
+++ b/compiler/rustc_trait_selection/src/traits/select/mod.rs
@@ -1192,6 +1192,8 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
                     ImplCandidate(def_id) if tcx.constness(def_id) == hir::Constness::Const => {}
                     // const param
                     ParamCandidate(trait_pred) if trait_pred.is_const_if_const() => {}
+                    // const projection
+                    ProjectionCandidate(_, ty::BoundConstness::ConstIfConst) => {}
                     // auto trait impl
                     AutoImplCandidate(..) => {}
                     // generator, this will raise error in other places
@@ -1399,7 +1401,7 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
     fn match_projection_obligation_against_definition_bounds(
         &mut self,
         obligation: &TraitObligation<'tcx>,
-    ) -> smallvec::SmallVec<[usize; 2]> {
+    ) -> smallvec::SmallVec<[(usize, ty::BoundConstness); 2]> {
         let poly_trait_predicate = self.infcx().resolve_vars_if_possible(obligation.predicate);
         let placeholder_trait_predicate =
             self.infcx().replace_bound_vars_with_placeholders(poly_trait_predicate);
@@ -1447,7 +1449,7 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
                             _ => false,
                         }
                     }) {
-                        return Some(idx);
+                        return Some((idx, pred.constness));
                     }
                 }
                 None
@@ -1683,9 +1685,9 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
                 | BuiltinCandidate { .. }
                 | TraitAliasCandidate(..)
                 | ObjectCandidate(_)
-                | ProjectionCandidate(_),
+                | ProjectionCandidate(..),
             ) => !is_global(cand),
-            (ObjectCandidate(_) | ProjectionCandidate(_), ParamCandidate(ref cand)) => {
+            (ObjectCandidate(_) | ProjectionCandidate(..), ParamCandidate(ref cand)) => {
                 // Prefer these to a global where-clause bound
                 // (see issue #50825).
                 is_global(cand)
@@ -1707,20 +1709,20 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
                 is_global(cand) && other.evaluation.must_apply_modulo_regions()
             }
 
-            (ProjectionCandidate(i), ProjectionCandidate(j))
+            (ProjectionCandidate(i, _), ProjectionCandidate(j, _))
             | (ObjectCandidate(i), ObjectCandidate(j)) => {
                 // Arbitrarily pick the lower numbered candidate for backwards
                 // compatibility reasons. Don't let this affect inference.
                 i < j && !needs_infer
             }
-            (ObjectCandidate(_), ProjectionCandidate(_))
-            | (ProjectionCandidate(_), ObjectCandidate(_)) => {
+            (ObjectCandidate(_), ProjectionCandidate(..))
+            | (ProjectionCandidate(..), ObjectCandidate(_)) => {
                 bug!("Have both object and projection candidate")
             }
 
             // Arbitrarily give projection and object candidates priority.
             (
-                ObjectCandidate(_) | ProjectionCandidate(_),
+                ObjectCandidate(_) | ProjectionCandidate(..),
                 ImplCandidate(..)
                 | ClosureCandidate
                 | GeneratorCandidate
@@ -1742,7 +1744,7 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
                 | TraitUpcastingUnsizeCandidate(_)
                 | BuiltinCandidate { .. }
                 | TraitAliasCandidate(..),
-                ObjectCandidate(_) | ProjectionCandidate(_),
+                ObjectCandidate(_) | ProjectionCandidate(..),
             ) => false,
 
             (&ImplCandidate(other_def), &ImplCandidate(victim_def)) => {
diff --git a/src/test/ui/rfc-2632-const-trait-impl/assoc-type-const-bound-usage.rs b/src/test/ui/rfc-2632-const-trait-impl/assoc-type-const-bound-usage.rs
new file mode 100644
index 0000000000000..780a510c500dc
--- /dev/null
+++ b/src/test/ui/rfc-2632-const-trait-impl/assoc-type-const-bound-usage.rs
@@ -0,0 +1,14 @@
+// check-pass
+#![feature(const_trait_impl)]
+
+#[const_trait]
+trait Foo {
+    type Assoc: ~const Foo;
+    fn foo() {}
+}
+
+const fn foo<T: ~const Foo>() {
+    <T as Foo>::Assoc::foo();
+}
+
+fn main() {}