diff --git a/COPYING b/COPYING
deleted file mode 100644
--- a/COPYING
+++ /dev/null
@@ -1,165 +0,0 @@
-		   GNU LESSER GENERAL PUBLIC LICENSE
-                       Version 3, 29 June 2007
-
- Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
- Everyone is permitted to copy and distribute verbatim copies
- of this license document, but changing it is not allowed.
-
-
-  This version of the GNU Lesser General Public License incorporates
-the terms and conditions of version 3 of the GNU General Public
-License, supplemented by the additional permissions listed below.
-
-  0. Additional Definitions. 
-
-  As used herein, "this License" refers to version 3 of the GNU Lesser
-General Public License, and the "GNU GPL" refers to version 3 of the GNU
-General Public License.
-
-  "The Library" refers to a covered work governed by this License,
-other than an Application or a Combined Work as defined below.
-
-  An "Application" is any work that makes use of an interface provided
-by the Library, but which is not otherwise based on the Library.
-Defining a subclass of a class defined by the Library is deemed a mode
-of using an interface provided by the Library.
-
-  A "Combined Work" is a work produced by combining or linking an
-Application with the Library.  The particular version of the Library
-with which the Combined Work was made is also called the "Linked
-Version".
-
-  The "Minimal Corresponding Source" for a Combined Work means the
-Corresponding Source for the Combined Work, excluding any source code
-for portions of the Combined Work that, considered in isolation, are
-based on the Application, and not on the Linked Version.
-
-  The "Corresponding Application Code" for a Combined Work means the
-object code and/or source code for the Application, including any data
-and utility programs needed for reproducing the Combined Work from the
-Application, but excluding the System Libraries of the Combined Work.
-
-  1. Exception to Section 3 of the GNU GPL.
-
-  You may convey a covered work under sections 3 and 4 of this License
-without being bound by section 3 of the GNU GPL.
-
-  2. Conveying Modified Versions.
-
-  If you modify a copy of the Library, and, in your modifications, a
-facility refers to a function or data to be supplied by an Application
-that uses the facility (other than as an argument passed when the
-facility is invoked), then you may convey a copy of the modified
-version:
-
-   a) under this License, provided that you make a good faith effort to
-   ensure that, in the event an Application does not supply the
-   function or data, the facility still operates, and performs
-   whatever part of its purpose remains meaningful, or
-
-   b) under the GNU GPL, with none of the additional permissions of
-   this License applicable to that copy.
-
-  3. Object Code Incorporating Material from Library Header Files.
-
-  The object code form of an Application may incorporate material from
-a header file that is part of the Library.  You may convey such object
-code under terms of your choice, provided that, if the incorporated
-material is not limited to numerical parameters, data structure
-layouts and accessors, or small macros, inline functions and templates
-(ten or fewer lines in length), you do both of the following:
-
-   a) Give prominent notice with each copy of the object code that the
-   Library is used in it and that the Library and its use are
-   covered by this License.
-
-   b) Accompany the object code with a copy of the GNU GPL and this license
-   document.
-
-  4. Combined Works.
-
-  You may convey a Combined Work under terms of your choice that,
-taken together, effectively do not restrict modification of the
-portions of the Library contained in the Combined Work and reverse
-engineering for debugging such modifications, if you also do each of
-the following:
-
-   a) Give prominent notice with each copy of the Combined Work that
-   the Library is used in it and that the Library and its use are
-   covered by this License.
-
-   b) Accompany the Combined Work with a copy of the GNU GPL and this license
-   document.
-
-   c) For a Combined Work that displays copyright notices during
-   execution, include the copyright notice for the Library among
-   these notices, as well as a reference directing the user to the
-   copies of the GNU GPL and this license document.
-
-   d) Do one of the following:
-
-       0) Convey the Minimal Corresponding Source under the terms of this
-       License, and the Corresponding Application Code in a form
-       suitable for, and under terms that permit, the user to
-       recombine or relink the Application with a modified version of
-       the Linked Version to produce a modified Combined Work, in the
-       manner specified by section 6 of the GNU GPL for conveying
-       Corresponding Source.
-
-       1) Use a suitable shared library mechanism for linking with the
-       Library.  A suitable mechanism is one that (a) uses at run time
-       a copy of the Library already present on the user's computer
-       system, and (b) will operate properly with a modified version
-       of the Library that is interface-compatible with the Linked
-       Version. 
-
-   e) Provide Installation Information, but only if you would otherwise
-   be required to provide such information under section 6 of the
-   GNU GPL, and only to the extent that such information is
-   necessary to install and execute a modified version of the
-   Combined Work produced by recombining or relinking the
-   Application with a modified version of the Linked Version. (If
-   you use option 4d0, the Installation Information must accompany
-   the Minimal Corresponding Source and Corresponding Application
-   Code. If you use option 4d1, you must provide the Installation
-   Information in the manner specified by section 6 of the GNU GPL
-   for conveying Corresponding Source.)
-
-  5. Combined Libraries.
-
-  You may place library facilities that are a work based on the
-Library side by side in a single library together with other library
-facilities that are not Applications and are not covered by this
-License, and convey such a combined library under terms of your
-choice, if you do both of the following:
-
-   a) Accompany the combined library with a copy of the same work based
-   on the Library, uncombined with any other library facilities,
-   conveyed under the terms of this License.
-
-   b) Give prominent notice with the combined library that part of it
-   is a work based on the Library, and explaining where to find the
-   accompanying uncombined form of the same work.
-
-  6. Revised Versions of the GNU Lesser General Public License.
-
-  The Free Software Foundation may publish revised and/or new versions
-of the GNU Lesser General Public License from time to time. Such new
-versions will be similar in spirit to the present version, but may
-differ in detail to address new problems or concerns.
-
-  Each version is given a distinguishing version number. If the
-Library as you received it specifies that a certain numbered version
-of the GNU Lesser General Public License "or any later version"
-applies to it, you have the option of following the terms and
-conditions either of that published version or of any later version
-published by the Free Software Foundation. If the Library as you
-received it does not specify a version number of the GNU Lesser
-General Public License, you may choose any version of the GNU Lesser
-General Public License ever published by the Free Software Foundation.
-
-  If the Library as you received it specifies that a proxy can decide
-whether future versions of the GNU Lesser General Public License shall
-apply, that proxy's public statement of acceptance of any version is
-permanent authorization for you to choose that version for the
-Library.
diff --git a/Data/BitSet.hs b/Data/BitSet.hs
--- a/Data/BitSet.hs
+++ b/Data/BitSet.hs
@@ -1,29 +1,34 @@
--- | An efficient membership-testing module, for types that can be mapped into
--- @Int@s.
+-- | A /bit set/ maintains a record of members from a type that can be mapped
+-- into (non-negative) @Int@s.  Supports insertion, deletion, size, and
+-- membership testing, and is completely pure (functional).
 --
--- The implementation is quite simple: we rely on the @Bits Integer@ instance
--- from @Data.Bits@ for the three main operations.  An advantage of this
--- library is the phantom parameter used in the BitSet type.  Since there is
--- no exported way to construct a value of type `BitSet' directly, the
--- interface we expose ensures client code will not typecheck if it confuses
--- two bit sets intended to keep track of different types.
+-- To use this library, simply supply a `Hash' instance for your data type.
+-- (See the `Hash' class for the relevant laws your instance must obey.)  Each
+-- operation requires at most one call to `hash'.  It is important that the
+-- values you intend to keep track of start from 0 and go up.  A value which
+-- `hash'es to @n@ corresponds to bit location @n@ in an @Integer@, and thus
+-- requires that @Integer@ to have at least @n@ bits.  Don't shoot yourself in
+-- the foot by `hash'ing to big @Int@s.
 --
--- It is important that the values you intend to keep track of start from 0
--- and go up.  Each @Int@ mapped to be hash corresponds to that bit location in
--- an @Integer@, and thus requires that @Integer@ to have at least that many
--- bits.  Don't shoot yourself in the foot.
+-- The implementation is quite simple: we rely on the @Bits Integer@ instance
+-- from @Data.Bits@.  An advantage of this library over simply using that
+-- @Bits@ instance is the phantom type parameter used in the `BitSet' type.
+-- The interface we expose ensures client code will not typecheck if it
+-- confuses two bit sets intended to keep track of different types.
 module Data.BitSet
     ( Hash(..)
     , BitSet
     , empty
+    , null
     , insert
     , delete
     , member
+    , size
     ) where
 
+import Prelude hiding ( null )
 import Data.Bits
 
-import Test.QuickCheck
 
 -- | Map a value to an non-negative @Int@.
 --
@@ -32,8 +37,8 @@
 -- the client code.  (We don't depend on equality, but the client code will
 -- certainly want to use the above sort of inference.)
 --
--- In fact, if your equivalence relation is @==@, the following quickcheck
--- test should pass, for arbitrary @x@ and @y@:
+-- In fact, if the relevant relation is @==@, the following quickcheck
+-- test should pass, for arbitrary @x@ and @y@ of type @a@:
 --
 -- @prop_hash x y =
 --     if hash x == hash y then x == y
@@ -43,9 +48,10 @@
 class Hash a where
     hash :: a -> Int
 
--- | The @Show@ instance kind of sucks.  It just shows the @Integer@
--- representation.  A good show would probably show all the present hashes.
-newtype BitSet a = BS { unBS :: Integer }
+-- | The @Show@ instance kind of sucks.  It just shows the size paired with
+-- the internal @Integer@ representation.  A good show would probably show all
+-- the present hashes.
+newtype BitSet a = BS { unBS :: (Int, Integer) }
     deriving (Eq)
 
 instance Show (BitSet a) where
@@ -54,6 +60,9 @@
 -- | The empty bit set.
 empty :: BitSet a
 
+-- | Is the bit set empty?
+null :: BitSet a -> Bool
+
 -- | /O(setBit on Integer)/ Insert an item into the bit set.
 insert :: Hash a => a -> BitSet a -> BitSet a
 
@@ -63,20 +72,35 @@
 -- | /O(testBit on Integer)/ Ask whether the item is in the bit set.
 member :: Hash a => a -> BitSet a -> Bool
 
+-- | /O(1)/ The number of elements in the bit set.
+size :: BitSet a -> Int
 
+
 -- * Implementation
 
-empty = BS 0
+empty = BS (0, 0)
 
+null (BS (n, _)) = n == 0
+
 {-# INLINE insert #-}
-insert x s = BS $ setBit (unBS s) (hash x)
+insert x s@(BS (count, i)) = BS $ (count', setBit i h)
+    where count' = if h `memHash` s then count else count+1
+          h      = hash x
 
 {-# INLINE delete #-}
-delete x s = BS $ clearBit (unBS s) (hash x)
+delete x s@(BS (count, i)) = BS $ (count', clearBit i h)
+    where count' = if h `memHash` s then count-1 else count
+          h      = hash x
 
 {-# INLINE member #-}
-member x s = testBit (unBS s) (hash x)
+member x s = hash x `memHash` s
+memHash :: Int -> BitSet a -> Bool
+{-# INLINE memHash #-}
+memHash h (BS (_, i)) = testBit i h
 
+{-# INLINE size #-}
+size (BS (count, _)) = count
+
 -- * Default instances
 
 instance Hash Int where
@@ -89,29 +113,4 @@
 -- instance Integral a => Hash a where
 --     hash = fromIntegral
 
--- * Quickcheck properties
-
-instance Arbitrary (BitSet a) where
-    arbitrary = sized $ \n -> return $ BS $ fromIntegral n
-
-prop_insert x s = xa `member` insert xa s
-    where xa = abs x :: Int
-
-prop_delete x s = not $ xa `member` delete xa s
-    where xa = abs x :: Int
-
-prop_insDelIdempotent x = empty == (delete xa . insert xa $ empty)
-    where xa = abs x :: Int
-
-prop_delDelIdempotent x s = delete xa s == (delete xa . delete xa $ s)
-    where xa = abs x :: Int
-
-prop_insInsIdempotent x s = insert xa s == (insert xa . insert xa $ s)
-    where xa = abs x :: Int
-
-prop_extensional xs = and $ map (`member` s) xsa
-    where s = foldr insert empty xsa
-          xsa = map abs xs :: [Int]
-
-prop_empty x = not $ xa `member` empty
-    where xa = abs x :: Int
+    
diff --git a/LICENSE b/LICENSE
new file mode 100644
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,165 @@
+		   GNU LESSER GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+
+  This version of the GNU Lesser General Public License incorporates
+the terms and conditions of version 3 of the GNU General Public
+License, supplemented by the additional permissions listed below.
+
+  0. Additional Definitions. 
+
+  As used herein, "this License" refers to version 3 of the GNU Lesser
+General Public License, and the "GNU GPL" refers to version 3 of the GNU
+General Public License.
+
+  "The Library" refers to a covered work governed by this License,
+other than an Application or a Combined Work as defined below.
+
+  An "Application" is any work that makes use of an interface provided
+by the Library, but which is not otherwise based on the Library.
+Defining a subclass of a class defined by the Library is deemed a mode
+of using an interface provided by the Library.
+
+  A "Combined Work" is a work produced by combining or linking an
+Application with the Library.  The particular version of the Library
+with which the Combined Work was made is also called the "Linked
+Version".
+
+  The "Minimal Corresponding Source" for a Combined Work means the
+Corresponding Source for the Combined Work, excluding any source code
+for portions of the Combined Work that, considered in isolation, are
+based on the Application, and not on the Linked Version.
+
+  The "Corresponding Application Code" for a Combined Work means the
+object code and/or source code for the Application, including any data
+and utility programs needed for reproducing the Combined Work from the
+Application, but excluding the System Libraries of the Combined Work.
+
+  1. Exception to Section 3 of the GNU GPL.
+
+  You may convey a covered work under sections 3 and 4 of this License
+without being bound by section 3 of the GNU GPL.
+
+  2. Conveying Modified Versions.
+
+  If you modify a copy of the Library, and, in your modifications, a
+facility refers to a function or data to be supplied by an Application
+that uses the facility (other than as an argument passed when the
+facility is invoked), then you may convey a copy of the modified
+version:
+
+   a) under this License, provided that you make a good faith effort to
+   ensure that, in the event an Application does not supply the
+   function or data, the facility still operates, and performs
+   whatever part of its purpose remains meaningful, or
+
+   b) under the GNU GPL, with none of the additional permissions of
+   this License applicable to that copy.
+
+  3. Object Code Incorporating Material from Library Header Files.
+
+  The object code form of an Application may incorporate material from
+a header file that is part of the Library.  You may convey such object
+code under terms of your choice, provided that, if the incorporated
+material is not limited to numerical parameters, data structure
+layouts and accessors, or small macros, inline functions and templates
+(ten or fewer lines in length), you do both of the following:
+
+   a) Give prominent notice with each copy of the object code that the
+   Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the object code with a copy of the GNU GPL and this license
+   document.
+
+  4. Combined Works.
+
+  You may convey a Combined Work under terms of your choice that,
+taken together, effectively do not restrict modification of the
+portions of the Library contained in the Combined Work and reverse
+engineering for debugging such modifications, if you also do each of
+the following:
+
+   a) Give prominent notice with each copy of the Combined Work that
+   the Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the Combined Work with a copy of the GNU GPL and this license
+   document.
+
+   c) For a Combined Work that displays copyright notices during
+   execution, include the copyright notice for the Library among
+   these notices, as well as a reference directing the user to the
+   copies of the GNU GPL and this license document.
+
+   d) Do one of the following:
+
+       0) Convey the Minimal Corresponding Source under the terms of this
+       License, and the Corresponding Application Code in a form
+       suitable for, and under terms that permit, the user to
+       recombine or relink the Application with a modified version of
+       the Linked Version to produce a modified Combined Work, in the
+       manner specified by section 6 of the GNU GPL for conveying
+       Corresponding Source.
+
+       1) Use a suitable shared library mechanism for linking with the
+       Library.  A suitable mechanism is one that (a) uses at run time
+       a copy of the Library already present on the user's computer
+       system, and (b) will operate properly with a modified version
+       of the Library that is interface-compatible with the Linked
+       Version. 
+
+   e) Provide Installation Information, but only if you would otherwise
+   be required to provide such information under section 6 of the
+   GNU GPL, and only to the extent that such information is
+   necessary to install and execute a modified version of the
+   Combined Work produced by recombining or relinking the
+   Application with a modified version of the Linked Version. (If
+   you use option 4d0, the Installation Information must accompany
+   the Minimal Corresponding Source and Corresponding Application
+   Code. If you use option 4d1, you must provide the Installation
+   Information in the manner specified by section 6 of the GNU GPL
+   for conveying Corresponding Source.)
+
+  5. Combined Libraries.
+
+  You may place library facilities that are a work based on the
+Library side by side in a single library together with other library
+facilities that are not Applications and are not covered by this
+License, and convey such a combined library under terms of your
+choice, if you do both of the following:
+
+   a) Accompany the combined library with a copy of the same work based
+   on the Library, uncombined with any other library facilities,
+   conveyed under the terms of this License.
+
+   b) Give prominent notice with the combined library that part of it
+   is a work based on the Library, and explaining where to find the
+   accompanying uncombined form of the same work.
+
+  6. Revised Versions of the GNU Lesser General Public License.
+
+  The Free Software Foundation may publish revised and/or new versions
+of the GNU Lesser General Public License from time to time. Such new
+versions will be similar in spirit to the present version, but may
+differ in detail to address new problems or concerns.
+
+  Each version is given a distinguishing version number. If the
+Library as you received it specifies that a certain numbered version
+of the GNU Lesser General Public License "or any later version"
+applies to it, you have the option of following the terms and
+conditions either of that published version or of any later version
+published by the Free Software Foundation. If the Library as you
+received it does not specify a version number of the GNU Lesser
+General Public License, you may choose any version of the GNU Lesser
+General Public License ever published by the Free Software Foundation.
+
+  If the Library as you received it specifies that a proxy can decide
+whether future versions of the GNU Lesser General Public License shall
+apply, that proxy's public statement of acceptance of any version is
+permanent authorization for you to choose that version for the
+Library.
diff --git a/bitset.cabal b/bitset.cabal
--- a/bitset.cabal
+++ b/bitset.cabal
@@ -1,10 +1,13 @@
 Name:                bitset
-Version:             0.5
+Version:             0.6
 Synopsis:            A functional data structure for efficient membership testing.
-Description:         A bit set is a data structure for keeping membership information efficiently.  This implementation uses Data.Bits on Integers, and thus should achieve reasonable speed.
+Description:
+        A /bit set/ maintains a record of members from a type that can be mapped
+        into (non-negative) @Int@s.  Supports insertion, deletion, size, and
+        membership testing, and is completely pure (functional).
 Category:            Data Structures
 License:             LGPL
-License-file:        COPYING
+License-file:        LICENSE
 Author:              Denis Bueno
 Maintainer:          Denis Bueno <dbueno@gmail.com>
 Stability:           provisional
@@ -12,4 +15,6 @@
 Build-type:          Simple
 
 Exposed-modules:     Data.BitSet
-Ghc-options:         -W
+Ghc-options:         -Wall
+Ghc-prof-options:    -prof -auto-all
+Extra-source-files:  tests/Properties.hs
diff --git a/tests/Properties.hs b/tests/Properties.hs
new file mode 100644
--- /dev/null
+++ b/tests/Properties.hs
@@ -0,0 +1,81 @@
+module Properties where
+
+import Prelude hiding ( null )
+import Data.BitSet
+import Data.Foldable ( foldl' )
+import Data.List ( nub )
+import Test.QuickCheck
+import qualified Data.List as List
+
+
+
+main :: IO ()
+main = do
+  check config prop_size
+  check config prop_size_insert
+  check config prop_size_delete
+  check config prop_insert
+  check config prop_delete
+  check config prop_insDelIdempotent
+  check config prop_delDelIdempotent
+  check config prop_insInsIdempotent
+  check config prop_extensional
+  check config prop_empty
+
+config = defaultConfig{ configMaxTest = 1000 }
+
+-- * Quickcheck properties
+
+prop_size xs =
+    trivial (List.null uxs) $
+    length uxs == size (foldr insert empty uxs)
+        where uxs = nub (map abs xs) :: [Int]
+
+prop_size_insert x s =
+    trivial (null s) $
+    if xa `member` s then size s == size s'
+    else size s + 1 == size s'
+  where s' = insert xa s
+        xa = abs x :: Int
+
+prop_size_delete x s =
+    trivial (null s) $
+    if xa `member` s then size s - 1 == size s'
+    else size s == size s'
+  where s' = delete xa s
+        xa = abs x :: Int
+
+prop_insert x s = xa `member` insert xa s
+    where xa = abs x :: Int
+
+prop_delete x s = not $ xa `member` delete xa s
+    where xa = abs x :: Int
+
+prop_insDelIdempotent x s =
+    classify (not (xa `member` s)) "passed guard" $
+    not (xa `member` s) ==>
+    s == (delete xa . insert xa) s
+  where xa = abs x :: Int
+
+prop_delDelIdempotent x s =
+    classify (xa `member` s) "x in s" $
+    classify (not (xa `member` s)) "x not in s" $
+    delete xa s == (delete xa . delete xa $ s)
+  where xa = abs x :: Int
+
+prop_insInsIdempotent x s = insert xa s == (insert xa . insert xa) s
+    where xa = abs x :: Int
+
+prop_extensional xs = and $ map (`member` s) xsa
+    where s   = foldr insert empty xsa
+          xsa = map abs xs :: [Int]
+
+prop_empty x = not $ xa `member` empty
+    where xa = abs x :: Int
+
+
+
+instance (Arbitrary a, Hash a) => Arbitrary (BitSet a) where
+    arbitrary = sized $ \n ->
+                do xs <- vector n
+                   return $ foldl' (flip insert) empty xs