diff --git a/collects/tests/typed-racket/succeed/pr11392.rkt b/collects/tests/typed-racket/succeed/pr11392.rkt
new file mode 100644
index 00000000..78a832ab
--- /dev/null
+++ b/collects/tests/typed-racket/succeed/pr11392.rkt
@@ -0,0 +1,12 @@
+#lang typed/racket
+(struct: foo ((n : Number)))
+(struct: bar ((n : Number)))
+
+
+(define-type foobar (U foo bar))
+(define-predicate foobar? foobar)
+
+(: baz ((List) -> "two"))
+
+(define (baz x)
+  (if (foobar? x) 2 "two"))
diff --git a/collects/typed-racket/types/remove-intersect.rkt b/collects/typed-racket/types/remove-intersect.rkt
index 5101253e..bbf00415 100644
--- a/collects/typed-racket/types/remove-intersect.rkt
+++ b/collects/typed-racket/types/remove-intersect.rkt
@@ -26,6 +26,10 @@
          [(list (Name: n) (Name: n*))
           (or (free-identifier=? n n*)
               (overlap (resolve-once t1) (resolve-once t2)))]
+         [(list _ (Name: _))
+           (overlap t1 (resolve-once t2))]
+         [(list (Name: _) _)
+           (overlap (resolve-once t1) t2)]
          [(list (? Mu?) _) (overlap (unfold t1) t2)]
          [(list _ (? Mu?)) (overlap t1 (unfold t2))]