diff --git a/examples/Build.hs b/examples/Build.hs
index b54f978..14c0dcb 100644
--- a/examples/Build.hs
+++ b/examples/Build.hs
@@ -2,7 +2,7 @@
 module Build where
 
 import Control.Selective
-import Control.Selective.Free.Rigid
+import Control.Selective.Rigid.Free
 
 -- See Section 3 of the paper:
 -- https://www.staff.ncl.ac.uk/andrey.mokhov/selective-functors.pdf
diff --git a/examples/Processor.hs b/examples/Processor.hs
index 42e7856..00a40c1 100644
--- a/examples/Processor.hs
+++ b/examples/Processor.hs
@@ -1,9 +1,8 @@
-{-# LANGUAGE ConstraintKinds, DeriveFunctor
-             , LambdaCase, FlexibleContexts, FlexibleInstances, GADTs #-}
+{-# LANGUAGE ConstraintKinds, DeriveFunctor, GADTs, FlexibleContexts, LambdaCase #-}
 module Processor where
 
 import Control.Selective
-import Control.Selective.Free.Rigid
+import Control.Selective.Rigid.Free
 import Data.Functor
 import Data.Int (Int16)
 import Data.Word (Word8)
diff --git a/examples/Teletype/Rigid.hs b/examples/Teletype/Rigid.hs
index 51b246a..1fe3eee 100644
--- a/examples/Teletype/Rigid.hs
+++ b/examples/Teletype/Rigid.hs
@@ -4,7 +4,7 @@ module Teletype.Rigid where
 import Prelude hiding (getLine, putStrLn)
 import qualified Prelude as IO
 import Control.Selective
-import Control.Selective.Free.Rigid
+import Control.Selective.Rigid.Free
 
 -- See Section 5.2 of the paper:
 -- https://www.staff.ncl.ac.uk/andrey.mokhov/selective-functors.pdf
diff --git a/selective.cabal b/selective.cabal
index cd4315d..e5f07ec 100644
--- a/selective.cabal
+++ b/selective.cabal
@@ -36,7 +36,8 @@ library
     hs-source-dirs:     src
     exposed-modules:    Control.Selective,
                         Control.Selective.Free,
-                        Control.Selective.Free.Rigid
+                        Control.Selective.Rigid.Free,
+                        Control.Selective.Rigid.Freer
     build-depends:      base         >= 4.7     && < 5,
                         containers   >= 0.5.5.1 && < 0.7,
                         transformers >= 0.4.2.0 && < 0.6
@@ -59,8 +60,6 @@ library
 test-suite test
     hs-source-dirs:     test, examples
     other-modules:      Build,
-                        FreerRigid,
-                        FasterFreerRigid,
                         Laws,
                         Parser,
                         Processor,
diff --git a/src/Control/Selective/Free/Rigid.hs b/src/Control/Selective/Rigid/Free.hs
similarity index 95%
rename from src/Control/Selective/Free/Rigid.hs
rename to src/Control/Selective/Rigid/Free.hs
index 19beb7c..a0e71e2 100644
--- a/src/Control/Selective/Free/Rigid.hs
+++ b/src/Control/Selective/Rigid/Free.hs
@@ -1,7 +1,7 @@
 {-# LANGUAGE GADTs, RankNTypes, TupleSections #-}
 -----------------------------------------------------------------------------
 -- |
--- Module     : Control.Selective.Free.Rigid
+-- Module     : Control.Selective.Rigid.Free
 -- Copyright  : (c) Andrey Mokhov 2018-2019
 -- License    : MIT (see the file LICENSE)
 -- Maintainer : andrey.mokhov@gmail.com
@@ -12,11 +12,11 @@
 -- and monads, introduced in this paper:
 -- https://www.staff.ncl.ac.uk/andrey.mokhov/selective-functors.pdf.
 --
--- This module defines /free rigid selective functors/, i.e. for selective
--- functors satisfying the property @\<*\> = apS@.
+-- This module defines /free rigid selective functors/. Rigid selective functors
+-- are those that satisfy the property @\<*\> = apS@.
 --
 -----------------------------------------------------------------------------
-module Control.Selective.Free.Rigid (
+module Control.Selective.Rigid.Free (
     -- * Free rigid selective functors
     Select (..), liftSelect,
 
diff --git a/test/FreerRigid.hs b/src/Control/Selective/Rigid/Freer.hs
similarity index 76%
rename from test/FreerRigid.hs
rename to src/Control/Selective/Rigid/Freer.hs
index 47544bb..c9413f9 100644
--- a/test/FreerRigid.hs
+++ b/src/Control/Selective/Rigid/Freer.hs
@@ -1,5 +1,24 @@
 {-# LANGUAGE DeriveFunctor, GADTs, RankNTypes #-}
-module FreerRigid (
+-----------------------------------------------------------------------------
+-- |
+-- Module     : Control.Selective.Rigid.Freer
+-- Copyright  : (c) Andrey Mokhov 2018-2019
+-- License    : MIT (see the file LICENSE)
+-- Maintainer : andrey.mokhov@gmail.com
+-- Stability  : experimental
+--
+-- This is a library for /selective applicative functors/, or just
+-- /selective functors/ for short, an abstraction between applicative functors
+-- and monads, introduced in this paper:
+-- https://www.staff.ncl.ac.uk/andrey.mokhov/selective-functors.pdf.
+--
+-- This module defines /freer rigid selective functors/. Rigid selective
+-- functors are those that satisfy the property @\<*\> = apS@. Compared to the
+-- "free" construction from "Control.Selective.Rigid.Free", this "freer"
+-- construction does not require the underlying base data type to be a functor.
+--
+-----------------------------------------------------------------------------
+module Control.Selective.Rigid.Freer (
     -- * Free rigid selective functors
     Select (..), liftSelect,
 
diff --git a/test/FasterFreerRigid.hs b/test/FasterFreerRigid.hs
deleted file mode 100644
index 76e6a07..0000000
--- a/test/FasterFreerRigid.hs
+++ /dev/null
@@ -1,82 +0,0 @@
-{-# LANGUAGE DeriveFunctor, GADTs, RankNTypes #-}
-module FasterFreerRigid (
-    -- * Free rigid selective functors
-    Select (..), liftSelect,
-
-    -- * Static analysis
-    getPure, getEffects, getNecessaryEffect, runSelect, foldSelect
-    ) where
-
-import Control.Monad.Trans.Except
-import Control.Selective
-import Data.Bifunctor
-import Data.Function
-import Data.Functor
-
--- Inspired by free applicative functors by Capriotti and Kaposi.
--- See: https://arxiv.org/pdf/1403.0749.pdf
-
--- Note: In the current implementation, 'select' costs O(N), where N is the
--- number of effects. It is possible to improve this to O(1) by using the idea
--- developed for free applicative functors by Dave Menendez, see this blog post:
--- https://www.eyrie.org/~zednenem/2013/05/27/freeapp
--- An example implementation can be found here:
--- http://hackage.haskell.org/package/free/docs/Control-Applicative-Free-Fast.html
-
--- | Free rigid selective functors.
-data Select f a where
-    Pure   :: a -> Select f a
-    Select :: (a -> Either (b -> c) c) -> Select f a -> f b -> Select f c
-
--- TODO: Prove that this is a lawful 'Functor'.
-instance Functor (Select f) where
-    fmap f (Pure a)       = Pure (f a)
-    fmap f (Select g x y) = Select (bimap (f.) f <$> g) x y -- O(1)
-
--- TODO: Prove that this is a lawful 'Applicative'.
-instance Applicative (Select f) where
-    pure  = Pure
-    (<*>) = apS -- Rigid selective functors
-
--- TODO: Prove that this is a lawful 'Selective'.
-instance Selective (Select f) where
-    select = selectBy (first (&))
-      where
-        selectBy :: (a -> Either (b -> c) c) -> Select f a -> Select f b -> Select f c
-        selectBy f x (Pure y)       = either ($y) id . f <$> x
-        selectBy f x (Select g y z) = Select id (selectBy h x y) z -- O(N)
-          where
-            h a = case f a of Right r -> Right (Right r)
-                              Left dr -> Left  (bimap (dr.) dr . g)
-
--- | Lift a functor into a free selective computation.
-liftSelect :: f a -> Select f a
-liftSelect f = Select (const $ Left id) (Pure ()) f
-
--- | Given a natural transformation from @f@ to @g@, this gives a canonical
--- natural transformation from @Select f@ to @g@.
-runSelect :: Selective g => (forall x. f x -> g x) -> Select f a -> g a
-runSelect _ (Pure a)       = pure a
-runSelect t (Select f x y) = select (f <$> runSelect t x) ((&) <$> t y)
-
--- | Concatenate all effects of a free selective computation.
-foldSelect :: Monoid m => (forall x. f x -> m) -> Select f a -> m
-foldSelect f = getOver . runSelect (Over . f)
-
--- | Extract the resulting value if there are no necessary effects.
-getPure :: Select f a -> Maybe a
-getPure = runSelect (const Nothing)
-
--- | Collect all possible effects in the order they appear in a free selective
--- computation.
-getEffects :: Functor f => Select f a -> [f ()]
-getEffects = foldSelect (pure . void)
-
--- | Extract the necessary effect from a free selective computation. Note: there
--- can be at most one effect that is statically guaranteed to be necessary.
-getNecessaryEffect :: Functor f => Select f a -> Maybe (f ())
-getNecessaryEffect = leftToMaybe . runExcept . runSelect (throwE . void)
-
-leftToMaybe :: Either a b -> Maybe a
-leftToMaybe (Left a) = Just a
-leftToMaybe _        = Nothing
diff --git a/test/Main.hs b/test/Main.hs
index 808cfe2..e6c858f 100644
--- a/test/Main.hs
+++ b/test/Main.hs
@@ -14,7 +14,7 @@ import Laws
 import Validation
 
 import qualified Control.Selective.Free       as F
-import qualified Control.Selective.Free.Rigid as FR
+import qualified Control.Selective.Rigid.Free as FR
 import qualified Teletype                     as F
 import qualified Teletype.Rigid               as FR