diff --git a/collects/tests/typed-scheme/fail/apply-dots.ss b/collects/tests/typed-scheme/fail/apply-dots.ss
new file mode 100644
index 00000000..6dde0cf9
--- /dev/null
+++ b/collects/tests/typed-scheme/fail/apply-dots.ss
@@ -0,0 +1,11 @@
+#lang typed-scheme
+
+(plambda: (a ...) ([z : String] . [w : Number])
+          (apply (case-lambda: (([x : Number] . [y : Number ... a]) x))
+                 w))
+
+(plambda: (a ...) ([z : String] . [w : Number])
+          (apply (case-lambda: (([x : Number] . [y : Number ... a]) x)
+                               (([x : String] [y : String] . [z : String]) 0)
+                               ([y : String] 0))
+                 w))
\ No newline at end of file
diff --git a/collects/tests/typed-scheme/succeed/apply-dots.ss b/collects/tests/typed-scheme/succeed/apply-dots.ss
new file mode 100644
index 00000000..506f11a7
--- /dev/null
+++ b/collects/tests/typed-scheme/succeed/apply-dots.ss
@@ -0,0 +1,19 @@
+#lang typed-scheme
+
+(plambda: (a ...) ([z : String] . [w : Number ... a])
+          (apply (lambda: ([x : Number] . [y : Number ... a]) x)
+                 1 w))
+
+(plambda: (a ...) ([z : String] . [w : Number ... a])
+          (apply (lambda: ([x : Number] . [y : Number]) x)
+                 1 w))
+
+(plambda: (a ...) ([z : String] . [w : Number])
+          (apply (lambda: ([x : Number] . [y : Number]) x)
+                 1 w))
+
+(plambda: (a ...) ([z : String] . [w : Number])
+          (apply (case-lambda: (([x : Number] . [y : Number ... a]) x)
+                               (([x : String] [y : String] . [z : String]) 0)
+                               ([y : Number] 0))
+                 w))
\ No newline at end of file