diff --git a/composition.cabal b/composition.cabal
--- a/composition.cabal
+++ b/composition.cabal
@@ -1,5 +1,5 @@
 name:                composition
-version:             1.0.0.1
+version:             1.0.1.0
 synopsis:            Combinators for unorthodox function composition
 
 license:             BSD3
@@ -24,4 +24,4 @@
 source-repository this
   type:     darcs
   location: http://patch-tag.com/r/DanBurton/composition
-  tag:      composition-1.0.0.1
+  tag:      composition-1.0.1.0
diff --git a/src/Data/Composition.hs b/src/Data/Composition.hs
--- a/src/Data/Composition.hs
+++ b/src/Data/Composition.hs
@@ -1,27 +1,54 @@
+-- | This module is for convenience and demonstrative purposes
+-- more than it is for providing actual value.
+-- I do not recommend that you rely on this module
+-- for performance-sensitive code.
+-- Because this module is not based on Prelude's (.),
+-- some chances at optimization might be missed by your compiler.
 module Data.Composition (
-  (.:),
-  (.*),
-  (.**),
-  (.***),
-  (.****),
-  (.*****),
-  (.******),
-  (.*******),
-  (.********),
-  compose2,
-  compose3,
-  compose4,
-  compose5,
-  compose6,
-  compose7,
-  compose8,
-  compose9
-) where
+  -- * Math
+    (∘)
+  
+  -- * Colons and dots
+  , (.:)
+  , (.:.)
+  , (.::)
+  , (.::.)
+  , (.:::)
+  , (.:::.)
+  , (.::::)
+  , (.::::.)
+  
+  -- * Asterisks
+  , (.*)
+  , (.**)
+  , (.***)
+  , (.****)
+  , (.*****)
+  , (.******)
+  , (.*******)
+  , (.********)
+  
+  -- * composeN
+  , compose1
+  , compose2
+  , compose3
+  , compose4
+  , compose5
+  , compose6
+  , compose7
+  , compose8
+  , compose9
+  
+  ) where
 
 -- Not exported. This is defined here to remove the dependency on base
 (.) :: (b -> c) -> (a -> b) -> a -> c
 (f . g) x = f (g x)
 
+-- | The mathematical symbol for function composition.
+(∘) :: (b -> c) -> (a -> b) -> a -> c
+(∘) = (.)
+
 -- | Compose two functions. @f .: g@ is similar to @f . g@
 -- except that @g@ will be fed /two/ arguments instead of one
 -- before handing its result to @f@.
@@ -47,7 +74,7 @@
 -- | Equivalent to '.:'
 -- 
 -- The pattern of appending asterisks is
--- more straightforward to extend to similar functions:
+-- straightforward to extend to similar functions:
 -- (compose2 = .*, compose3 = .**, etc).
 -- However, @.:@ has been commonly adopted amongst Haskellers,
 -- and the need for compose3 and beyond is rare in practice.
@@ -64,6 +91,10 @@
 (.*******) = (.) . (.******)
 (.********) = (.) . (.*******)
 
+-- | @composeN f g@ means give @g@ @N@ inputs
+-- and then pass its result to @f@.
+compose1 :: (b -> c) -> (a -> b) -> a -> c
+compose1 = (.)
 
 compose2 :: (c -> d) -> (a -> b -> c) -> a -> b -> d
 compose2 = (.*)
@@ -78,3 +109,16 @@
 compose8 = (.*******)
 compose9 = (.********)
 
+-- | One compact pattern for composition operators is to
+-- "count the dots after the first one",
+-- which begins with the common '.:', and proceeds by first
+-- appending another @.@ and then replacing it with @:@
+(.:.) :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e
+(.:.) = (.**)
+
+(.::) = (.***)
+(.::.) = (.****)
+(.:::) = (.*****)
+(.:::.) = (.******)
+(.::::) = (.*******)
+(.::::.) = (.********)