diff --git a/compiler/rustc_trait_selection/src/traits/project.rs b/compiler/rustc_trait_selection/src/traits/project.rs
index b3e5df4da0a9f..5c2c49d8f1c89 100644
--- a/compiler/rustc_trait_selection/src/traits/project.rs
+++ b/compiler/rustc_trait_selection/src/traits/project.rs
@@ -1381,7 +1381,23 @@ fn confirm_callable_candidate<'cx, 'tcx>(
         ty: ret_type,
     });
 
-    confirm_param_env_candidate(selcx, obligation, predicate, false)
+    let Progress { ty, mut obligations } =
+        confirm_param_env_candidate(selcx, obligation, predicate, false);
+    if !ty.references_error() {
+        let sized_trait = tcx.lang_items().sized_trait().unwrap(); // FIXME--unwrap
+        let sized_predicate = ty::Binder::dummy(ty::TraitRef {
+            def_id: sized_trait,
+            substs: tcx.mk_substs_trait(ty, &[]),
+        })
+        .without_const()
+        .to_predicate(tcx);
+        let cause = obligation.cause.clone();
+        let depth = obligation.recursion_depth;
+        let param_env = obligation.param_env;
+        let obligation = Obligation::with_depth(cause, depth + 1, param_env, sized_predicate);
+        obligations.push(obligation);
+    }
+    Progress { ty, obligations }
 }
 
 fn confirm_param_env_candidate<'cx, 'tcx>(
diff --git a/src/test/ui/fn/issue-82633-2.rs b/src/test/ui/fn/issue-82633-2.rs
new file mode 100644
index 0000000000000..68e04d1610b2b
--- /dev/null
+++ b/src/test/ui/fn/issue-82633-2.rs
@@ -0,0 +1,7 @@
+fn weird_situation<F: FnOnce() -> str>() {
+    println!("if this is reachable, there’s a function type with unsized Output type `str`");
+}
+
+fn main() {
+    weird_situation::<fn() -> str>()
+}
diff --git a/src/test/ui/fn/issue-82633.rs b/src/test/ui/fn/issue-82633.rs
new file mode 100644
index 0000000000000..dba48914d00fa
--- /dev/null
+++ b/src/test/ui/fn/issue-82633.rs
@@ -0,0 +1,18 @@
+#![feature(unboxed_closures)]
+
+trait A {
+    fn a()
+    where
+        Self: Sized;
+}
+
+fn foo<F: FnOnce<()>>()
+where
+    F::Output: A,
+{
+    F::Output::a()
+}
+
+fn main() {
+    foo::<fn() -> dyn A>()
+}