diff --git a/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions2.rkt b/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions2.rkt
new file mode 100644
index 00000000..9c923800
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions2.rkt
@@ -0,0 +1,9 @@
+#lang typed/scheme #:optimize
+
+(require racket/unsafe/ops)
+
+;; function with multiple complex args
+(let ((f (lambda: ((x : Inexact-Complex) (y : Inexact-Complex))
+                  (+ x y))))
+  (f (+ 1.0+2.0i 2.0+4.0i)
+     3.0+6.0i))
diff --git a/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions3.rkt b/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions3.rkt
new file mode 100644
index 00000000..9bc0f44c
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions3.rkt
@@ -0,0 +1,9 @@
+#lang typed/scheme #:optimize
+
+(require racket/unsafe/ops)
+
+;; function with a mix of complex and non-complex args
+(let ((f (lambda: ((x : Inexact-Complex) (y : Float))
+                  (+ x y))))
+  (f (+ 1.0+2.0i 2.0+4.0i)
+     3.0))
diff --git a/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions4.rkt b/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions4.rkt
new file mode 100644
index 00000000..eef46901
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions4.rkt
@@ -0,0 +1,9 @@
+#lang typed/scheme #:optimize
+
+(require racket/unsafe/ops)
+
+;; function with a mix of complex and non-complex args, non-complex first
+(let ((f (lambda: ((y : Float) (x : Inexact-Complex))
+                  (+ x y))))
+  (f 3.0
+     (+ 1.0+2.0i 2.0+4.0i)))
diff --git a/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions5.rkt b/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions5.rkt
new file mode 100644
index 00000000..7b685942
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/generic/unboxed-let-functions5.rkt
@@ -0,0 +1,10 @@
+#lang typed/scheme #:optimize
+
+(require racket/unsafe/ops)
+
+;; invalid: f "escapes", according to our analysis
+(letrec: ((f : (Inexact-Complex -> Inexact-Complex)
+             (lambda: ((x : Inexact-Complex))
+                      (let: ((y : (Inexact-Complex -> Inexact-Complex) f))
+                            x))))
+         (f (+ 1.0+2.0i 2.0+4.0i)))