diff --git a/collects/typed-racket/infer/infer-unit.rkt b/collects/typed-racket/infer/infer-unit.rkt
index 0a94076d..a577b9b1 100644
--- a/collects/typed-racket/infer/infer-unit.rkt
+++ b/collects/typed-racket/infer/infer-unit.rkt
@@ -27,12 +27,12 @@
 (define (seen-before s t)
   (cons (Type-seq s) (Type-seq t)))
 (define/cond-contract (remember s t A)
- (Values/c Values/c
+ ((or/c AnyValues? Values/c) (or/c AnyValues? Values/c)
   (listof (cons/c exact-nonnegative-integer? exact-nonnegative-integer?)) . -> .
   (listof (cons/c exact-nonnegative-integer? exact-nonnegative-integer?)))
  (cons (seen-before s t) A))
 (define/cond-contract (seen? s t)
- (Values/c Values/c . -> . any/c)
+ ((or/c AnyValues? Values/c) (or/c AnyValues? Values/c) . -> . any/c)
  (member (seen-before s t) (current-seen)))
 
 
@@ -587,7 +587,7 @@
 ;; Y : (listof symbol?) - index variables that must have entries
 ;; R : Type/c - result type into which we will be substituting
 (define/cond-contract (subst-gen C Y R)
-  (cset? (listof symbol?) (or/c Values/c ValuesDots?) . -> . (or/c #f substitution/c))
+  (cset? (listof symbol?) (or/c Values/c AnyValues? ValuesDots?) . -> . (or/c #f substitution/c))
   (define var-hash (free-vars-hash (free-vars* R)))
   (define idx-hash (free-vars-hash (free-idxs* R)))
   ;; v : Symbol - variable for which to check variance
@@ -721,7 +721,7 @@
   (define/cond-contract (infer X Y S T R [expected #f])
     (((listof symbol?) (listof symbol?) (listof Type/c) (listof Type/c)
       (or/c #f Values/c ValuesDots?))
-     ((or/c #f Values/c ValuesDots?))
+     ((or/c #f Values/c AnyValues? ValuesDots?))
      . ->* . (or/c boolean? substitution/c))
     (with-handlers ([exn:infer? (lambda _ #f)])
       (let* ([expected-cset (if expected
diff --git a/collects/typed-racket/infer/signatures.rkt b/collects/typed-racket/infer/signatures.rkt
index 7fc10ae5..fbea98be 100644
--- a/collects/typed-racket/infer/signatures.rkt
+++ b/collects/typed-racket/infer/signatures.rkt
@@ -41,7 +41,7 @@
                             ;; range
                             (or/c #f Values/c ValuesDots?))
                            ;; optional expected type
-                           ((or/c #f Values/c ValuesDots?))
+                           ((or/c #f Values/c AnyValues? ValuesDots?))
                            . ->* . any)]
    [cond-contracted infer/vararg ((;; variables from the forall
                                    (listof symbol?)
@@ -56,7 +56,7 @@
                                    ;; range
                                    (or/c #f Values/c ValuesDots?))
                                   ;; [optional] expected type
-                                  ((or/c #f Values/c ValuesDots?)) . ->* . any)]
+                                  ((or/c #f Values/c AnyValues? ValuesDots?)) . ->* . any)]
    [cond-contracted infer/dots (((listof symbol?)
                                  symbol?
                                  (listof Values/c)
@@ -64,4 +64,4 @@
                                  Values/c
                                  (or/c Values/c ValuesDots?)
                                  (listof symbol?))
-                                (#:expected (or/c #f Values/c ValuesDots?)) . ->* . any)]))
+                                (#:expected (or/c #f Values/c AnyValues? ValuesDots?)) . ->* . any)]))
diff --git a/collects/typed-racket/typecheck/tc-app-helper.rkt b/collects/typed-racket/typecheck/tc-app-helper.rkt
index 83295c74..fd1db072 100644
--- a/collects/typed-racket/typecheck/tc-app-helper.rkt
+++ b/collects/typed-racket/typecheck/tc-app-helper.rkt
@@ -92,7 +92,7 @@
    ((syntax? syntax? Type/c (c:listof (c:listof Type/c)) (c:listof (c:or/c #f Type/c))
      (c:listof (c:or/c #f (c:cons/c Type/c (c:or/c c:natural-number/c symbol?))))
      (c:listof SomeValues/c) (c:listof tc-results?) (c:or/c #f Type/c) c:any/c)
-    (#:expected (c:or/c #f tc-results?) #:return tc-results?
+    (#:expected (c:or/c #f tc-results/c) #:return tc-results?
      #:msg-thunk (c:-> string? string?))
     . c:->* . tc-results/c)
 
diff --git a/collects/typed-racket/typecheck/tc-funapp.rkt b/collects/typed-racket/typecheck/tc-funapp.rkt
index 2481f811..3d94c837 100644
--- a/collects/typed-racket/typecheck/tc-funapp.rkt
+++ b/collects/typed-racket/typecheck/tc-funapp.rkt
@@ -67,7 +67,7 @@
       ;; if nothing matched, error
       (domain-mismatches
        f-stx args-stx t doms rests drests rngs argtys #f #f
-       #:expected expected #:return (or expected (ret (Un)))
+       #:expected expected #:return (if (tc-results? expected) expected (ret (Un)))
        #:msg-thunk (lambda (dom)
                      (string-append
                       "No function domains matched in function application:\n"