diff --git a/src/librustc_mir/borrow_check/error_reporting.rs b/src/librustc_mir/borrow_check/error_reporting.rs
index e3fc591bda847..d8a3cf9947024 100644
--- a/src/librustc_mir/borrow_check/error_reporting.rs
+++ b/src/librustc_mir/borrow_check/error_reporting.rs
@@ -217,6 +217,17 @@ impl<'cx, 'gcx, 'tcx> MirBorrowckCtxt<'cx, 'gcx, 'tcx> {
                         break;
                     }
                 }
+                if let ty::TyKind::Param(param_ty) = ty.sty {
+                    let tcx = self.infcx.tcx;
+                    let generics = tcx.generics_of(self.mir_def_id);
+                    let def_id = generics.type_param(&param_ty, tcx).def_id;
+                    if let Some(sp) = tcx.hir().span_if_local(def_id) {
+                        err.span_label(
+                            sp,
+                            "consider adding a `Copy` constraint to this type argument",
+                        );
+                    }
+                }
                 if note {
                     err.note(&format!(
                         "move occurs because {} has type `{}`, \
diff --git a/src/test/ui/borrowck/two-phase-nonrecv-autoref.nll.stderr b/src/test/ui/borrowck/two-phase-nonrecv-autoref.nll.stderr
index 0e99e158eda02..d026f81b7aad6 100644
--- a/src/test/ui/borrowck/two-phase-nonrecv-autoref.nll.stderr
+++ b/src/test/ui/borrowck/two-phase-nonrecv-autoref.nll.stderr
@@ -10,6 +10,8 @@ LL |         f(f(10));
 error[E0382]: use of moved value: `*f`
   --> $DIR/two-phase-nonrecv-autoref.rs:69:11
    |
+LL |     fn twice_ten_so<F: FnOnce(i32) -> i32>(f: Box<F>) {
+   |                     - consider adding a `Copy` constraint to this type argument
 LL |         f(f(10));
    |         - ^ value used here after move
    |         |
diff --git a/src/test/ui/issues/issue-34721.stderr b/src/test/ui/issues/issue-34721.stderr
index b4e274b1c7019..2ed7b543e713c 100644
--- a/src/test/ui/issues/issue-34721.stderr
+++ b/src/test/ui/issues/issue-34721.stderr
@@ -2,7 +2,9 @@ error[E0382]: use of moved value: `x`
   --> $DIR/issue-34721.rs:27:9
    |
 LL |     pub fn baz<T: Foo>(x: T) -> T {
-   |                        - move occurs because `x` has type `T`, which does not implement the `Copy` trait
+   |                -       - move occurs because `x` has type `T`, which does not implement the `Copy` trait
+   |                |
+   |                consider adding a `Copy` constraint to this type argument
 LL |         if 0 == 1 {
 LL |             bar::bar(x.zero())
    |                      - value moved here