diff --git a/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/static-contracts/combinators/derived.rkt b/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/static-contracts/combinators/derived.rkt
index d95a361879..fcef3a14f2 100644
--- a/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/static-contracts/combinators/derived.rkt
+++ b/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/static-contracts/combinators/derived.rkt
@@ -5,7 +5,7 @@
 ;; Ex: (listof/sc any/sc) => list?/sc
 
 (require "simple.rkt" "structural.rkt"
-         (for-template racket/base racket/set racket/promise))
+         (for-template racket/base racket/list racket/set racket/promise))
 (provide (all-defined-out))
 
 (define identifier?/sc (flat/sc #'identifier?))
@@ -13,6 +13,7 @@
 (define syntax?/sc (flat/sc #'syntax?))
 (define promise?/sc (flat/sc #'promise?))
 
+(define cons?/sc (flat/sc #'cons?))
 (define list?/sc (flat/sc #'list?))
 
 (define set?/sc (flat/sc #'set?))
diff --git a/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/static-contracts/optimize.rkt b/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/static-contracts/optimize.rkt
index a51eb39383..0bee1d0fbf 100644
--- a/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/static-contracts/optimize.rkt
+++ b/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/static-contracts/optimize.rkt
@@ -39,6 +39,7 @@
     ;[(hash/sc: key/sc (none/sc:)) empty-hash/sc]
 
     ;; any/sc cases
+    [(cons/sc: (any/sc:) (any/sc:)) cons?/sc]
     [(listof/sc: (any/sc:)) list?/sc]
     [(list/sc: (and scs (any/sc:)) ...) (list-length/sc (length scs))]
     [(vectorof/sc: (any/sc:)) vector?/sc]
diff --git a/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/unit-tests/static-contract-optimizer-tests.rkt b/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/unit-tests/static-contract-optimizer-tests.rkt
index 78022dd324..947aa6fd50 100644
--- a/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/unit-tests/static-contract-optimizer-tests.rkt
+++ b/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/unit-tests/static-contract-optimizer-tests.rkt
@@ -271,4 +271,8 @@
       #:pos any/sc
       #:neg list?/sc)
 
+    (check-optimize (cons/sc any/sc list?/sc)
+      #:pos any/sc
+      #:neg (cons/sc any/sc list?/sc))
+
     ))