diff --git a/cf.cabal b/cf.cabal
--- a/cf.cabal
+++ b/cf.cabal
@@ -1,5 +1,5 @@
 name:                cf
-version:             0.3
+version:             0.4
 synopsis:            Exact real arithmetic using continued fractions
 license:             MIT   
 license-file:        LICENSE
@@ -9,6 +9,10 @@
 category:            Math
 build-type:          Simple
 cabal-version:       >=1.10
+description:
+            Continued fraction arithmetic using Gosper's algorithm for the
+            basic operations, and Vuillemin and Lester's techniques for
+            transcendental functions.
 
 source-repository head
   type: git
diff --git a/src/Math/ContinuedFraction.hs b/src/Math/ContinuedFraction.hs
--- a/src/Math/ContinuedFraction.hs
+++ b/src/Math/ContinuedFraction.hs
@@ -2,6 +2,10 @@
 {-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE TypeFamilies #-}
+-- |
+-- A continued fraction whose terms may be positive, negative or
+-- zero. The methods in @Floating@ are supported, with the exception
+-- of @asin@, @acos@ and @atan@.
 module Math.ContinuedFraction (
   CF,
   CF'(..),
@@ -279,6 +283,8 @@
                       d0, d1) d = (base * (n0 - d0*d), base * (n1 - d1*d),
                                    d0,                 d1)
 
+-- | Produce the (possibly infinite) decimal expansion of a continued
+-- fraction
 cfString :: CF -> String
 cfString (CF []) = "Infinity"
 cfString cf | cf < 0 = '-' : cfString (-cf)
@@ -307,6 +313,8 @@
                                                           Nothing
           checkValid _ = Nothing
 
+-- | Convert a continued fraction whose terms are continued fractions
+-- into an ordinary continued fraction with integer terms
 cfcf :: CF' CF -> CF
 cfcf = hom (1, 0, 0, 1)
 
diff --git a/src/Math/ContinuedFraction/Simple.hs b/src/Math/ContinuedFraction/Simple.hs
--- a/src/Math/ContinuedFraction/Simple.hs
+++ b/src/Math/ContinuedFraction/Simple.hs
@@ -1,7 +1,9 @@
+-- |
+-- A "standard" continued fraction, whose terms are all either
+-- positive or negative.
 module Math.ContinuedFraction.Simple
   (
     CF,
-    digits,
     showCF,
     sqrt2,
     exp1
@@ -104,9 +106,11 @@
                                                else
                                                  bihom (bihomAbsorbY bh y) (CF (x:xs)) (CF ys)
 
+-- | The square root of 2
 sqrt2 :: CF
 sqrt2 = CF $ 1 : repeat 2
 
+-- | e
 exp1 :: CF
 exp1 = CF (2 : concatMap triple [1..])
   where triple n = [1, 2 * n, 1]
@@ -174,7 +178,7 @@
 rationalDigits :: Rational -> [Integer]
 rationalDigits 0 = []
 rationalDigits r = let d = num `quot` den in
-                   d : rationalDigits (fromInteger 10 * (r - fromInteger d))
+                   d : rationalDigits (10 * (r - fromInteger d))
   where num = numerator r
         den = denominator r
 
@@ -189,7 +193,8 @@
                       d0, d1) d = (10 * (n0 - d0*d), 10 * (n1 - d1*d),
                                    d0,               d1)
 
--- | Produce a decimal representation of a number
+-- | Produce the (possibly infinite) decimal expansion of a continued
+-- fraction
 showCF :: CF -> String
 showCF cf | cf < 0 = "-" ++ show (-cf)
 showCF (CF [i])   = show i
diff --git a/tests/Tests.hs b/tests/Tests.hs
--- a/tests/Tests.hs
+++ b/tests/Tests.hs
@@ -1,10 +1,9 @@
-{-# LANGUAGE TemplateHaskell, FlexibleInstances #-}
+{-# LANGUAGE TemplateHaskell #-}
 module Main where
 
 import Data.Maybe
-import Data.Ratio
 
-import Math.ContinuedFraction
+import Math.ContinuedFraction.Effective
 import Math.ContinuedFraction.Interval
 
 import Test.QuickCheck
@@ -12,37 +11,28 @@
 import Test.Framework.TH
 import Test.Framework.Providers.QuickCheck2
 
-instance Arbitrary (Extended Rational) where
+instance Arbitrary Extended where
   arbitrary = do
     b <- arbitrary :: Gen Bool
     if b then
       return Infinity
-    else do
-      n <- choose (-10, 10)
-      return $ Finite (n % 1)
+    else
+      fmap Finite arbitrary
 
-instance Arbitrary (Interval Rational) where
+instance Arbitrary Interval where
   arbitrary = do
-    (i, s) <- suchThat arbitrary (\(i,s) -> i /= s) :: Gen (Extended Rational, Extended Rational)
+    (i, s) <- suchThat arbitrary (\(i,s) -> i /= s) :: Gen (Extended, Extended)
     return $ Interval i s
 
+prop_sensibleEmittable x = isJust $ existsEmittable (primitiveBound x)
+  where types = x :: Integer
+
 prop_sensiblePrimitiveBound x = fromInteger x `elementOf` primitiveBound x
   where types = x :: Integer
 
 prop_sensibleMergeInterval a b = a `subset` ab && b `subset` ab
-  where types = (a :: Interval Rational, b :: Interval Rational)
+  where types = (a :: Interval, b :: Interval)
         ab = a `mergeInterval` b
-
-finitePrimitiveBounds (CF cf) = zipWith boundHom homs (map primitiveBound cf)
-  where homs = scanl homAbsorb (1,0,0,1) cf
-
-prop_primitiveBoundsContain a b = all ((Finite $ a + b) `elementOf`) $ finitePrimitiveBounds (valueToCF a + valueToCF b)
-  where types = (a :: Rational, b :: Rational)
-
-prop_sensibleEuclidean i = case existsEmittable i of
-                            Just n -> i `subset` primitiveBound n
-                            Nothing -> True
-  where types = i :: Interval Rational
 
 main :: IO ()
 main = $defaultMainGenerator