diff --git a/collects/tests/typed-racket/succeed/het-vec.rkt b/collects/tests/typed-racket/succeed/het-vec.rkt
index 7d4bc354..7edbb819 100644
--- a/collects/tests/typed-racket/succeed/het-vec.rkt
+++ b/collects/tests/typed-racket/succeed/het-vec.rkt
@@ -8,3 +8,8 @@
 
 (ann (vector-ref x 1) String)
 (ann (vector-ref x y) Symbol)
+
+(: ref : Integer -> (U Number String Symbol))
+(define (ref i) (vector-ref x i))
+
+(ann (vector-ref #(1.0 2.0) 0) Flonum)
diff --git a/collects/tests/typed-racket/xfail/inst+special-case.rkt b/collects/tests/typed-racket/xfail/inst+special-case.rkt
new file mode 100644
index 00000000..bf38d91e
--- /dev/null
+++ b/collects/tests/typed-racket/xfail/inst+special-case.rkt
@@ -0,0 +1,10 @@
+#lang typed/racket
+
+;; In tc-app, code paths for annotated operators and special case typing rules
+;; (for, e.g., `vector-ref') are mutually exclusive.
+;; The annotated operator case matches first and falls back to the regular
+;; application rules, skipping the special cases.
+;; This example, because it uses a heterogenous vector, needs the special type
+;; rule, and therefore doesn't typecheck.
+
+(ann ((inst vector-ref String) #(1.0) 0) Float)