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 0000000000..9c9238003a
--- /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 0000000000..9bc0f44c9a
--- /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 0000000000..eef4690197
--- /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 0000000000..7b6859422c
--- /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)))
diff --git a/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions2.rkt b/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions2.rkt
new file mode 100644
index 0000000000..10d68ed889
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions2.rkt
@@ -0,0 +1,22 @@
+#lang racket
+
+(require racket/unsafe/ops)
+
+;; function with multiple complex args
+(let ((f (lambda (unboxed-real-1 unboxed-real-2 unboxed-imag-3 unboxed-imag-4)
+           (let*-values (((unboxed-gensym-5) (unsafe-fl+ unboxed-real-1 unboxed-real-2))
+                         ((unboxed-gensym-6) (unsafe-fl+ unboxed-imag-3 unboxed-imag-4)))
+             (unsafe-make-flrectangular unboxed-gensym-5 unboxed-gensym-6)))))
+  (let*-values (((unboxed-gensym-1) 1.0+2.0i)
+                ((unboxed-gensym-2) (unsafe-flreal-part unboxed-gensym-1))
+                ((unboxed-gensym-3) (unsafe-flimag-part unboxed-gensym-1))
+                ((unboxed-gensym-4) 2.0+4.0i)
+                ((unboxed-gensym-5) (unsafe-flreal-part unboxed-gensym-4))
+                ((unboxed-gensym-6) (unsafe-flimag-part unboxed-gensym-4))
+                ((unboxed-gensym-7) (unsafe-fl+ unboxed-gensym-2 unboxed-gensym-5))
+                ((unboxed-gensym-8) (unsafe-fl+ unboxed-gensym-3 unboxed-gensym-6))
+                ((unboxed-gensym-9) 3.0+6.0i)
+                ((unboxed-gensym-10) (unsafe-flreal-part unboxed-gensym-9))
+                ((unboxed-gensym-11) (unsafe-flimag-part unboxed-gensym-9)))
+    (f unboxed-gensym-7 unboxed-gensym-10 unboxed-gensym-8 unboxed-gensym-11)))
+(void)
diff --git a/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions3.rkt b/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions3.rkt
new file mode 100644
index 0000000000..2973ecf0cc
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions3.rkt
@@ -0,0 +1,20 @@
+#lang racket
+
+(require racket/unsafe/ops)
+
+;; function with a mix of complex and non-complex args
+(let ((f (lambda (unboxed-real-1 unboxed-imag-2 y)
+           (let*-values (((unboxed-gensym-3) y)
+                         ((unboxed-gensym-4) (unsafe-fl+ unboxed-real-1 unboxed-gensym-3))
+                         ((unboxed-gensym-5) unboxed-imag-2))
+             (unsafe-make-flrectangular unboxed-gensym-4 unboxed-gensym-5)))))
+  (let*-values (((unboxed-gensym-1) 1.0+2.0i)
+                ((unboxed-gensym-2) (unsafe-flreal-part unboxed-gensym-1))
+                ((unboxed-gensym-3) (unsafe-flimag-part unboxed-gensym-1))
+                ((unboxed-gensym-4) 2.0+4.0i)
+                ((unboxed-gensym-5) (unsafe-flreal-part unboxed-gensym-4))
+                ((unboxed-gensym-6) (unsafe-flimag-part unboxed-gensym-4))
+                ((unboxed-gensym-7) (unsafe-fl+ unboxed-gensym-2 unboxed-gensym-5))
+                ((unboxed-gensym-8) (unsafe-fl+ unboxed-gensym-3 unboxed-gensym-6)))
+    (f unboxed-gensym-7 unboxed-gensym-8 3.0)))
+(void)
diff --git a/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions4.rkt b/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions4.rkt
new file mode 100644
index 0000000000..2973ecf0cc
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions4.rkt
@@ -0,0 +1,20 @@
+#lang racket
+
+(require racket/unsafe/ops)
+
+;; function with a mix of complex and non-complex args
+(let ((f (lambda (unboxed-real-1 unboxed-imag-2 y)
+           (let*-values (((unboxed-gensym-3) y)
+                         ((unboxed-gensym-4) (unsafe-fl+ unboxed-real-1 unboxed-gensym-3))
+                         ((unboxed-gensym-5) unboxed-imag-2))
+             (unsafe-make-flrectangular unboxed-gensym-4 unboxed-gensym-5)))))
+  (let*-values (((unboxed-gensym-1) 1.0+2.0i)
+                ((unboxed-gensym-2) (unsafe-flreal-part unboxed-gensym-1))
+                ((unboxed-gensym-3) (unsafe-flimag-part unboxed-gensym-1))
+                ((unboxed-gensym-4) 2.0+4.0i)
+                ((unboxed-gensym-5) (unsafe-flreal-part unboxed-gensym-4))
+                ((unboxed-gensym-6) (unsafe-flimag-part unboxed-gensym-4))
+                ((unboxed-gensym-7) (unsafe-fl+ unboxed-gensym-2 unboxed-gensym-5))
+                ((unboxed-gensym-8) (unsafe-fl+ unboxed-gensym-3 unboxed-gensym-6)))
+    (f unboxed-gensym-7 unboxed-gensym-8 3.0)))
+(void)
diff --git a/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions5.rkt b/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions5.rkt
new file mode 100644
index 0000000000..e1daeb27f3
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/hand-optimized/unboxed-let-functions5.rkt
@@ -0,0 +1,18 @@
+#lang racket
+
+(require racket/unsafe/ops)
+
+;; invalid: f "escapes", according to our analysis
+(letrec ((f (lambda (x)
+              (let ((y f))
+                x))))
+  (f (let*-values (((unboxed-gensym-1) 1.0+2.0i)
+                   ((unboxed-gensym-2) (unsafe-flreal-part unboxed-gensym-1))
+                   ((unboxed-gensym-3) (unsafe-flimag-part unboxed-gensym-1))
+                   ((unboxed-gensym-4) 2.0+4.0i)
+                   ((unboxed-gensym-5) (unsafe-flreal-part unboxed-gensym-4))
+                   ((unboxed-gensym-6) (unsafe-flimag-part unboxed-gensym-4))
+                   ((unboxed-gensym-7) (unsafe-fl+ unboxed-gensym-2 unboxed-gensym-5))
+                   ((unboxed-gensym-8) (unsafe-fl+ unboxed-gensym-3 unboxed-gensym-6)))
+       (unsafe-make-flrectangular unboxed-gensym-7 unboxed-gensym-8))))
+(void)
diff --git a/collects/tests/typed-scheme/optimizer/non-optimized/unboxed-let-functions2.rkt b/collects/tests/typed-scheme/optimizer/non-optimized/unboxed-let-functions2.rkt
new file mode 100644
index 0000000000..6454579e6f
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/non-optimized/unboxed-let-functions2.rkt
@@ -0,0 +1,9 @@
+#lang typed/scheme
+
+(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/non-optimized/unboxed-let-functions3.rkt b/collects/tests/typed-scheme/optimizer/non-optimized/unboxed-let-functions3.rkt
new file mode 100644
index 0000000000..e6e2963214
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/non-optimized/unboxed-let-functions3.rkt
@@ -0,0 +1,9 @@
+#lang typed/scheme
+
+(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/non-optimized/unboxed-let-functions4.rkt b/collects/tests/typed-scheme/optimizer/non-optimized/unboxed-let-functions4.rkt
new file mode 100644
index 0000000000..d6e565f643
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/non-optimized/unboxed-let-functions4.rkt
@@ -0,0 +1,9 @@
+#lang typed/scheme
+
+(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/non-optimized/unboxed-let-functions5.rkt b/collects/tests/typed-scheme/optimizer/non-optimized/unboxed-let-functions5.rkt
new file mode 100644
index 0000000000..2c9889a60c
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/non-optimized/unboxed-let-functions5.rkt
@@ -0,0 +1,10 @@
+#lang typed/scheme
+
+(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)))