diff --git a/collects/tests/typed-scheme/optimizer/tests/invalid-derived-pair.rkt b/collects/tests/typed-scheme/optimizer/tests/invalid-derived-pair.rkt
new file mode 100644
index 00000000..89a4ca52
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/tests/invalid-derived-pair.rkt
@@ -0,0 +1,14 @@
+#;
+()
+
+#lang typed/racket #:optimize
+
+;; can't optimize, the lists may not be long enough
+(: f ((Listof Integer) -> Integer))
+(define (f x)
+  (cadr x))
+(: g ((Listof Integer) -> Integer))
+(define (g x)
+  (if (null? x)
+      0
+      (cadr x)))