diff --git a/collects/typed-scheme/test.ss b/collects/typed-scheme/test.ss
index ea249073..097675c0 100644
--- a/collects/typed-scheme/test.ss
+++ b/collects/typed-scheme/test.ss
@@ -43,4 +43,9 @@
 ;; Error
 #;#{(case-lambda: [() 1]
                 [([x : Number]) x]) :: String}
+#{(lambda: ([x : Number]) 1) :: (Number -> Number)}
+#{(lambda: ([x : Number]) 1) :: Any}
+#{(lambda: ([x : Number]) 1) :: (Integer -> Any)}
+#{(lambda: ([x : Number]) x) :: (Number -> Number)}
+#{(lambda: ([x : Number]) x) :: (Integer -> Any)}
 
diff --git a/collects/typed-scheme/typecheck/tc-expr-unit.ss b/collects/typed-scheme/typecheck/tc-expr-unit.ss
index 075cc095..c1fb45ec 100644
--- a/collects/typed-scheme/typecheck/tc-expr-unit.ss
+++ b/collects/typed-scheme/typecheck/tc-expr-unit.ss
@@ -136,24 +136,24 @@
   (match* (tr1 expected)
     [((tc-results: t1) (tc-results: t2))
      (unless (andmap subtype t1 t2)
-       (tc-error/expr "Expected ~a, but got ~a" t2 t1))
+       (tc-error/expr "1 Expected ~a, but got ~a" t2 t1))
      expected]
     [((tc-result1: t1 f o) (? Type? t2))
      (unless (subtype t1 t2)
-       (tc-error/expr "Expected ~a, but got ~a" t2 t1))
+       (tc-error/expr "1 Expected ~a, but got ~a" t2 t1))
      (ret t2 f o)]
     [((? Type? t1) (tc-result1: t2 (FilterSet: (list) (list)) (Empty:)))
      (unless (subtype t1 t2)
-       (tc-error/expr "Expected ~a, but got ~a" t2 t1))
+       (tc-error/expr "3 Expected ~a, but got ~a" t2 t1))
      t1]
     [((? Type? t1) (tc-result1: t2 f o))
      (if (subtype t1 t2)
          (tc-error/expr "Expected result with filter ~a and object ~a, got ~a" f o t1)
-         (tc-error/expr "Expected ~a, but got ~a" t2 t1))
+         (tc-error/expr "4 Expected ~a, but got ~a" t2 t1))
      t1]
     [((? Type? t1) (? Type? t2))
      (unless (subtype t1 t2)
-       (tc-error/expr "Expected ~a, but got ~a" t2 t1))
+       (tc-error/expr "5 Expected ~a, but got ~a" t2 t1))
      expected]))
 
 (define (tc-expr/check/type form expected)
diff --git a/collects/typed-scheme/types/subtype.ss b/collects/typed-scheme/types/subtype.ss
index 14f2ab3c..4c154e5c 100644
--- a/collects/typed-scheme/types/subtype.ss
+++ b/collects/typed-scheme/types/subtype.ss
@@ -125,6 +125,12 @@
     (match* (s t)
       ;; top for functions is above everything
       [(_ (top-arr:)) A0]
+      ;; the really simple case
+      [((arr: s1 s2 #f #f '())
+        (arr: t1 t2 #f #f '()))
+       (subtype-seq A0
+                    (subtypes* t1 s1)
+                    (subtype* s2 t2))]
       [((arr: s1 s2 #f #f s-kws)
         (arr: t1 t2 #f #f t-kws))
        (subtype-seq A0
@@ -301,6 +307,9 @@
               ;; trivial case for Result
               [(list (Result: t f o) (Result: t* f o))
                (subtype* A0 t t*)]
+              ;; we can ignore interesting results
+              [(list (Result: t f o) (Result: t* (LFilterSet: (list) (list)) (LEmpty:)))
+               (subtype* A0 t t*)]
 	      ;; single values shouldn't actually happen, but they're just like the type
 	      [(list t (Values: (list t*))) (int-err "BUG - singleton values type~a" (make-Values (list t*)))]
 	      [(list (Values: (list t)) t*) (int-err "BUG - singleton values type~a" (make-Values (list t)))]