diff --git a/collects/tests/racket/optimize.rktl b/collects/tests/racket/optimize.rktl
index d4268f919e..2c9b5fcab9 100644
--- a/collects/tests/racket/optimize.rktl
+++ b/collects/tests/racket/optimize.rktl
@@ -3124,6 +3124,27 @@
           (if (<= y x) (* x y) '-))))
 
 ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Make sure that a procedure used in a first-order
+;; way bound by `letrec' can have a typed closure element:
+
+(let ([e `(module m racket/base
+            (provide f)
+            (define (f v)
+              (let ([y (vector-length v)])
+                (letrec ([foo (lambda (r)
+                                (if (zero? r)
+                                    y
+                                    (foo (sub1 r))))])
+                  foo))))]
+      [o (open-output-bytes)])
+  (write (compile e) o)
+  (parameterize ([current-namespace (make-base-namespace)])
+    (eval
+     (parameterize ([read-accept-compiled #t])
+       (read (open-input-bytes (get-output-bytes o)))))
+    (((dynamic-require ''m 'f) (vector 1)) 0)))
+
+;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 
 
 (report-errs)
diff --git a/src/racket/src/validate.c b/src/racket/src/validate.c
index efd6cc50a8..ac697b7564 100644
--- a/src/racket/src/validate.c
+++ b/src/racket/src/validate.c
@@ -1812,6 +1812,7 @@ static int validate_expr(Mz_CPort *port, Scheme_Object *expr,
   case scheme_letrec_type:
     {
       Scheme_Letrec *l = (Scheme_Letrec *)expr;
+      Scheme_Closure_Data *data;
       int i, c;
 
       c = l->count;
@@ -1830,10 +1831,20 @@ static int validate_expr(Mz_CPort *port, Scheme_Object *expr,
           scheme_ill_formed_code(port);
 #endif
 	stack[delta + i] = VALID_VAL;
-        if (SCHEME_CLOSURE_DATA_FLAGS(((Scheme_Closure_Data *)l->procs[i])) & CLOS_HAS_TYPED_ARGS) {
-          procs = scheme_hash_tree_set(as_nonempty_procs(procs),
-                                       scheme_make_integer(delta + i),
-                                       l->procs[i]);
+        data = (Scheme_Closure_Data *)l->procs[i];
+        if (SCHEME_CLOSURE_DATA_FLAGS(data) & CLOS_HAS_TYPED_ARGS) {
+          /* If any arguments (as opposed to closure slots) are typed, then
+             add the procedure to `procs': */
+          int j;
+          for (j = data->num_params; j--; ) {
+            if (scheme_boxmap_get(data->closure_map, j, data->closure_size))
+              break;
+          }
+          if (j >= 0) {
+            procs = scheme_hash_tree_set(as_nonempty_procs(procs),
+                                         scheme_make_integer(delta + i),
+                                         l->procs[i]);
+          }
         }
       }