diff --git a/Test/Arrow.lean b/Test/Arrow.lean
index a0bfc31..1970f2f 100644
--- a/Test/Arrow.lean
+++ b/Test/Arrow.lean
@@ -1,16 +1,35 @@
 import Qpf
 
+universe u v w
+
 /-- info: MvQPF.Arrow ?α : CurriedTypeFun 1 -/
 #guard_msgs in
   #check MvQPF.Arrow ?α
 
-data Arrow (α : Type _) β
+data Arrow (α : Type) β : Type u
   | mk : (α → β) → Arrow α β
 
 /-- info: Arrow : Type → CurriedTypeFun 1 -/
 #guard_msgs in
   #check (Arrow : Type → Type → Type)
 
--- Types generated by `data` are not as polymorphic as they could/should be,
---   so the following does not yet work:
--- `#check (Arrow : Type 1 → Type 1 → Type 1)`
+/-- info: Arrow.Shape : Type u → Type v → Type w → Type w -/
+#guard_msgs in #check (Arrow.Shape : Type u → Type v → Type w → Type w)
+
+/-- info: Arrow.Base : Type → TypeFun 2 -/
+#guard_msgs in #check (Arrow.Base : Type → TypeFun.{u, u} 2)
+
+#synth MvQPF (Arrow.Base _ : TypeFun.{0} 2)
+-- ^^^ We know that the `Base` is a QPF for universe 0
+
+#synth MvQPF (Arrow.Base _ : TypeFun.{1} 2)
+-- ^^^ But, somehow we can't synthesize this fact for higher universes
+
+#check (Arrow.Uncurried : Type → TypeFun.{1} 1)
+-- ^^^ Which, presumably, is why `Uncurried` is *not* polymorphic
+
+
+
+/-- info: Arrow : Type → CurriedTypeFun 1 -/
+#guard_msgs in
+  #check (Arrow : Type → Type u → Type u)