diff --git a/CHANGES.md b/CHANGES.md
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -1,6 +1,11 @@
 Changelog for singletons project
 ================================
 
+2.4.1
+-----
+* Restore the `TyCon1`, `TyCon2`, etc. types. It turns out that the new
+`TyCon` doesn't work with kind-polymorphic tycons.
+
 2.4
 ---
 * Require GHC 8.4.
diff --git a/singletons.cabal b/singletons.cabal
--- a/singletons.cabal
+++ b/singletons.cabal
@@ -1,5 +1,5 @@
 name:           singletons
-version:        2.4
+version:        2.4.1
                 -- Remember to bump version in the Makefile as well
 cabal-version:  >= 1.10
 synopsis:       A framework for generating singleton types
@@ -38,7 +38,7 @@
 source-repository this
   type:     git
   location: https://github.com/goldfirere/singletons.git
-  tag:      v2.4
+  tag:      v2.4.1
 
 library
   hs-source-dirs:     src
diff --git a/src/Data/Singletons.hs b/src/Data/Singletons.hs
--- a/src/Data/Singletons.hs
+++ b/src/Data/Singletons.hs
@@ -48,6 +48,7 @@
 
   -- ** Defunctionalization
   TyFun, type (~>),
+  TyCon1, TyCon2, TyCon3, TyCon4, TyCon5, TyCon6, TyCon7, TyCon8,
   TyCon, Apply, type (@@),
 
   -- ** Defunctionalized singletons
diff --git a/src/Data/Singletons/Internal.hs b/src/Data/Singletons/Internal.hs
--- a/src/Data/Singletons/Internal.hs
+++ b/src/Data/Singletons/Internal.hs
@@ -181,17 +181,10 @@
 type a @@ b = Apply a b
 infixl 9 @@
 
--- | Wrapper for converting the normal type-level arrow into a '~>'.
--- For example, given:
---
--- > data Nat = Zero | Succ Nat
--- > type family Map (a :: a ~> b) (a :: [a]) :: [b]
--- >   Map f '[] = '[]
--- >   Map f (x ': xs) = Apply f x ': Map f xs
---
--- We can write:
---
--- > Map (TyCon Succ) [Zero, Succ Zero]
+-- | Workhorse for the 'TyCon1', etc., types. This can be used directly
+-- in place of any of the @TyConN@ types, but it will work only with
+-- /monomorphic/ types. When GHC#14645 is fixed, this should fully supersede
+-- the @TyConN@ types.
 data family TyCon :: (k1 -> k2) -> unmatchable_fun
 -- That unmatchable_fun should really be a function of k1 and k2,
 -- but GHC 8.4 doesn't support type family calls in the result kind
@@ -211,6 +204,32 @@
   ApplyTyCon f x                     = f x
 
 type instance Apply (TyCon f) x = ApplyTyCon f x
+
+-- | Wrapper for converting the normal type-level arrow into a '~>'.
+-- For example, given:
+--
+-- > data Nat = Zero | Succ Nat
+-- > type family Map (a :: a ~> b) (a :: [a]) :: [b]
+-- >   Map f '[] = '[]
+-- >   Map f (x ': xs) = Apply f x ': Map f xs
+--
+-- We can write:
+--
+-- > Map (TyCon1 Succ) [Zero, Succ Zero]
+type TyCon1 = (TyCon :: (k1 -> k2) -> (k1 ~> k2))
+
+-- | Similar to 'TyCon1', but for two-parameter type constructors.
+type TyCon2 = (TyCon :: (k1 -> k2 -> k3) -> (k1 ~> k2 ~> k3))
+type TyCon3 = (TyCon :: (k1 -> k2 -> k3 -> k4) -> (k1 ~> k2 ~> k3 ~> k4))
+type TyCon4 = (TyCon :: (k1 -> k2 -> k3 -> k4 -> k5) -> (k1 ~> k2 ~> k3 ~> k4 ~> k5))
+type TyCon5 = (TyCon :: (k1 -> k2 -> k3 -> k4 -> k5 -> k6)
+                     -> (k1 ~> k2 ~> k3 ~> k4 ~> k5 ~> k6))
+type TyCon6 = (TyCon :: (k1 -> k2 -> k3 -> k4 -> k5 -> k6 -> k7)
+                     -> (k1 ~> k2 ~> k3 ~> k4 ~> k5 ~> k6 ~> k7))
+type TyCon7 = (TyCon :: (k1 -> k2 -> k3 -> k4 -> k5 -> k6 -> k7 -> k8)
+                     -> (k1 ~> k2 ~> k3 ~> k4 ~> k5 ~> k6 ~> k7 ~> k8))
+type TyCon8 = (TyCon :: (k1 -> k2 -> k3 -> k4 -> k5 -> k6 -> k7 -> k8 -> k9)
+                     -> (k1 ~> k2 ~> k3 ~> k4 ~> k5 ~> k6 ~> k7 ~> k8 ~> k9))
 
 ----------------------------------------------------------------------
 ---- Defunctionalized Sing instance and utilities --------------------