diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,5 +1,9 @@
 # Changelog for polysemy-composite
 
+## v0.1.4.0
+
+* Add `runMethodologyRMap`, `pickCoRecConstructor`, `fmapCMethodology`.
+
 ## v0.1.3.0
 
 * Add `separateRecInitial`, `stripRecInitial`, `stripRecInitial`, `endRecInitial`.
diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -4,3 +4,7 @@
 [polysemy-methodology](https://hackage.haskell.org/package/polysemy-methodology)
 in conjunction with
 [composite](https://hackage.haskell.org/package/composite-base).
+
+In order make best use of these, you should also bring in
+[polysemy-vinyl](https://hackage.haskell.org/package/polysemy-vinyl)
+and [polysemy-extra](https://hackage.haskell.org/package/polysemy-extra).
diff --git a/polysemy-methodology-composite.cabal b/polysemy-methodology-composite.cabal
--- a/polysemy-methodology-composite.cabal
+++ b/polysemy-methodology-composite.cabal
@@ -5,7 +5,7 @@
 -- see: https://github.com/sol/hpack
 
 name:           polysemy-methodology-composite
-version:        0.1.3.0
+version:        0.1.4.0
 synopsis:       Functions for using polysemy-methodology with composite.
 category:       Polysemy Vinyl Composite
 author:         Daniel Firth
diff --git a/src/Polysemy/Methodology/Composite.hs b/src/Polysemy/Methodology/Composite.hs
--- a/src/Polysemy/Methodology/Composite.hs
+++ b/src/Polysemy/Methodology/Composite.hs
@@ -13,15 +13,18 @@
 {-# LANGUAGE LambdaCase          #-}
 {-# LANGUAGE GADTs               #-}
 {-# LANGUAGE PolyKinds           #-}
+{-# LANGUAGE RankNTypes          #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE TypeApplications    #-}
 {-# LANGUAGE TypeOperators       #-}
 module Polysemy.Methodology.Composite (
-  runCoRecMethodologyAsCases
+  runMethodologyRmap
+, runCoRecMethodologyAsCases
 , runCoRecMethodologyAsCases'
 , diffractMethodology
 , diffractMethodology'
 , runInputCase'
+, pickCoRecConstructor
 , separateRecInitial
 , separateRecInitial'
 , stripRecInitial
@@ -32,6 +35,8 @@
 , separateRecTerminal'
 , stripRecTerminal
 , endRecTerminal
+, fmapCMethodology
+, fmapCMethodology'
 ) where
 
 import Control.Arrow
@@ -43,6 +48,17 @@
 import Polysemy.Input
 import Polysemy.Methodology
 
+-- | Run a `Methodology` between two `Rec`s according to a natural transformation
+-- between the interpretation functors.
+--
+-- @since 0.1.4.0
+runMethodologyRmap :: forall f g xs r a. RMap xs =>
+                      (forall y. f y -> g y)
+                   -> Sem (Methodology (Rec f xs) (Rec g xs) ': r) a
+                   -> Sem r a
+runMethodologyRmap f = runMethodologyPure (rmap f)
+{-# INLINE runMethodologyRmap #-}
+
 -- | Run a `Methodology` from a `CoRec` to an `Input` of `Cases'`. You can then use `Polysemy.Vinyl.separateRecInput` and `Polysemy.Vinyl.stripRecInput`
 -- to deal with the cases individually.
 --
@@ -116,6 +132,17 @@
 runInputCase' f = runInputConst (Case' f)
 {-# INLINE runInputCase' #-}
 
+-- | Take a `Methodology` into a `CoRec` and choose a constructor.
+--
+-- @since 0.1.4.0
+pickCoRecConstructor :: forall x f b xs r a. x ∈ xs =>
+                        Sem (Methodology b (CoRec f xs) ': r) a
+                     -> Sem (Methodology b (f x) ': r) a
+pickCoRecConstructor = cutMethodology'
+                   >>> rotateEffects2
+                   >>> runMethodologyPure CoVal
+{-# INLINE pickCoRecConstructor #-}
+
 -- | Factor a `Methodology` with a `Rec` in the result by a `Methodology` to the first variable.
 --
 -- @since 0.1.3.0
@@ -244,3 +271,24 @@
 endRecTerminal = interpret \case
   Process _ -> return mempty
 {-# INLINE endRecTerminal #-}
+
+-- | Like `fmapMethodology`, but used with a `Compose`d functor to strip the top
+-- layer from the functor.
+--
+-- @since 0.1.4.0
+fmapCMethodology :: forall f g h b c r a. Traversable f =>
+                     Sem (Methodology ((f :. g) b) ((f :. h) c) ': r) a
+                  -> Sem (Methodology (g b) (h c) ': r) a
+fmapCMethodology = reinterpret \case
+  Process b -> Compose <$> traverse (process @(g b) @(h c)) (getCompose b)
+{-# INLINE fmapCMethodology #-}
+
+-- | Reinterpreting version of `fmapCMethodology`.
+--
+-- @since 0.1.4.0
+fmapCMethodology' :: forall f g h b c r a. Traversable f =>
+                     Sem (Methodology ((f :. g) b) ((f :. h) c) ': r) a
+                  -> Sem (Methodology (g b) (h c) ': r) a
+fmapCMethodology' = reinterpret \case
+  Process b -> Compose <$> traverse (process @(g b) @(h c)) (getCompose b)
+{-# INLINE fmapCMethodology' #-}