diff --git a/CHANGES b/CHANGES
new file mode 100644
--- /dev/null
+++ b/CHANGES
@@ -0,0 +1,23 @@
+0.1.0.2
+=======
+
+- CIE XYZ to CIE L*a*b* formula implemented.
+- CIE L*a*b* to CIE XYZ formula implemented.
+- Implemented better fractional values in the formulas gleaned from
+  this website: [CIE Conversion Mathematics](http://rip94550.wordpress.com/2011/07/04/color-cielab-and-tristimulus-xyz/).
+- Comprehensive QuickCheck tests finished and pass with a lossless
+  conversion at 11 decimal places.
+
+0.1.0.1
+=======
+
+- SRGB to CIE XYZ formula implemented.
+- CIE XYZ to SRGB formula implemented.
+- Comprehensive QuickCheck tests finished and pass (conversion is lossless).
+
+0.1.0.0
+=======
+
+- Package set up, types figured out.
+- Research on different color representations, illuminants,
+  chromaticity, etc...
diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -7,6 +7,11 @@
 use in stylesheets and I wanted the same thing for use in [Clay](http://fvisser.nl/clay/) (also for
 [Bentonite](https://github.com/ixmatus/bentonite)).
 
+## Colour Module
+
+There is some overlap with the Haskell Colour Module that already exists; however, this library is filling a couple of
+needs the other doesn't satisfy. I also want to have a cleaner API to work with.
+
 ## Supported Algorithms
 
 - sRGB -> CIE XYZ
@@ -14,10 +19,13 @@
 
 ## Roadmap
 
-### 1.0.0
+### 0.1.0.2
+Make sure all of the conversion formulas convert losslessly at an acceptable level of precision.
+
+### 1.0.0.0
 Implementation of conversions for all the CIE color representations and a converter for HEX to SRGB (trivial).
 
-### 1.1.0
+### 1.1.0.0
 Implementations for
 
 - color mixing
@@ -26,5 +34,6 @@
 - hue
 - saturation
 - inversion
-
+[General Color Formulas, Data, and Algorithms](http://www.brucelindbloom.com/index.html?Info.html)
+[CIE Conversion Mathematics](http://rip94550.wordpress.com/2011/07/04/color-cielab-and-tristimulus-xyz/)
 [Conversion Algorithm Sources](http://www.easyrgb.com/index.php?X=MATH&H=01)
diff --git a/prizm.cabal b/prizm.cabal
--- a/prizm.cabal
+++ b/prizm.cabal
@@ -1,11 +1,11 @@
 Name:                prizm
-Version:             0.1.0.1
+Version:             0.1.0.2
 Synopsis:            A haskell library for computing with colors
 
 Description:         Prizm can convert between many different color
                      representations; notably the sRGB and CIE
                      representations. Future versions will
-                     implementations for mutating colors as well.
+                     have implementations for mutating colors as well.
 
 Homepage:            https://github.com/ixmatus/prizm
 License:             BSD3
@@ -24,6 +24,7 @@
 extra-source-files:
     LICENSE
     README.md
+    CHANGES
 
 source-repository head
   type:     git
@@ -33,12 +34,30 @@
   hs-source-dirs: src
   default-language: Haskell2010
   exposed-modules:
-    Data.Prizm
     Data.Prizm.Types
     Data.Prizm.Color.Transform
     Data.Prizm.Color.SRGB
     Data.Prizm.Color.CIE
+    Data.Prizm.Color.Matrices.RGB
+    Data.Prizm.Color.Matrices.XYZ
   
   ghc-options: -Wall
   
   build-depends: base ==4.5.*
+
+test-suite tests
+  type:           exitcode-stdio-1.0
+  hs-source-dirs: tests
+  main-is:        QC.hs
+  other-modules:  QC.SRGB
+--                  QC.Text
+
+  ghc-options:
+    -Wall -threaded -rtsopts
+
+  build-depends:
+    prizm,
+    base >= 4,
+    QuickCheck >= 2.4,
+    test-framework >= 0.4,
+    test-framework-quickcheck2 >= 0.2
diff --git a/src/Data/Prizm.hs b/src/Data/Prizm.hs
deleted file mode 100644
--- a/src/Data/Prizm.hs
+++ /dev/null
@@ -1,12 +0,0 @@
-module Data.Prizm
-(
-  module Data.Prizm.Types
-, module Data.Prizm.Color.Transform
-, module Data.Prizm.Color.SRGB
-, module Data.Prizm.Color.CIE
-) where
-
-import Data.Prizm.Types
-import Data.Prizm.Color.Transform
-import Data.Prizm.Color.CIE
-import Data.Prizm.Color.SRGB
diff --git a/src/Data/Prizm/Color/CIE.hs b/src/Data/Prizm/Color/CIE.hs
--- a/src/Data/Prizm/Color/CIE.hs
+++ b/src/Data/Prizm/Color/CIE.hs
@@ -1,33 +1,76 @@
 module Data.Prizm.Color.CIE
 (
   toRGB
+, toRGBMatrix
+, toLAB
+, toXYZ
 ) where
 
+import Control.Applicative
+
 import Data.Prizm.Types
 import Data.Prizm.Color.Transform
+import Data.Prizm.Color.Matrices.XYZ
 
-import Control.Applicative
+-- 2deg observer, d65 illuminant
+-- [x,y,z]
+refWhite :: [Double]
+refWhite = [95.047, 100.000, 108.883]
 
-matrix :: [[Double]]
-matrix = [
-  [3.2406, (-1.5372), (-0.4986)],
-  [(-0.9689), 1.8758, 0.0415],
-  [0.0557, (-0.2040), 1.0570]]
+-- | exact rational of the "0.008856" value.
+v1 :: Double
+v1 = (6/29) ** 3
 
--- | @transform@ transform an XYZ integer to be computed against
+-- | exact rational of the "7.787" value.
+v2 :: Double
+v2 = 1/3 * ((29/6) ** 2)
+
+-- | @transformRGB@ transform an XYZ integer to be computed against
 -- the xyzToRGB matrix.
-transform :: Double -> Integer
-transform v | v > 0.0031308 = min (truncate ((1.055 * (v ** (1 / 2.4)) - 0.055) * 255)) 255
-            | otherwise     = min (truncate ((12.92 * v) * 255)) 255
+transformRGB :: Double -> Integer
+transformRGB v | v > 0.0031308 = min (round ((1.055 * (v ** (1 / 2.4)) - 0.055) * 255)) 255
+               | otherwise     = min (round ((12.92 * v) * 255)) 255
 
+transformLAB :: Double -> Double
+transformLAB v | v > v1 = v ** (1/3)
+               | otherwise    = (v2 * v) + (16 / 116)
+
+transformXYZ :: Double -> Double
+transformXYZ v | cv > v1 = cv
+               | otherwise     = (v - 16 / 116) / v2
+    where cv = v**3
+
 -- | @toRGB@ convert a CIE color to an SRGB color.
 -- 
 -- Once I've implemented CIE L*a*b -> XYZ and vice-versa functions
 -- then I'll introduce the type exhaustively here to handle any CIE
 -- color -> SRGB conversion.
-toRGB :: CIE -> SRGB
---toRGB (LAB _ _ _) = Nothing
-toRGB (XYZ x y z) =
+toRGB :: CIE -> RGB
+toRGB = (toRGBMatrix d65SRGB)
+
+toRGBMatrix :: XYZtoRGB -> CIE -> RGB
+toRGBMatrix m (LAB l a b) = toRGBMatrix m (toXYZ (LAB l a b))
+toRGBMatrix m (XYZ x y z) =
     let t = ZipList ((/100) <$> [x,y,z])
-        [r,g,b] = (transform) <$> ((zipTransform t) <$> matrix)
-    in SRGB r g b
+        [r,g,b] = (transformRGB) <$> ((zipTransform t) <$> m)
+    in RGB r g b
+
+toLAB :: CIE -> CIE
+toLAB (LAB l a b) = LAB l a b
+toLAB (XYZ x y z) =
+    let v = getZipList $ ZipList ((/) <$> [x,y,z]) <*> ZipList refWhite
+        [tx,ty,tz] = (transformLAB) <$> v
+        l = (116 * ty) - 16
+        a = 500 * (tx - ty)
+        b = 200 * (ty - tz)
+    in LAB l a b
+
+toXYZ :: CIE -> CIE
+toXYZ (XYZ x y z) = XYZ x y z
+toXYZ (LAB l a b) =
+    let y = (l + 16) / 116
+        x = a / 500 + y
+        z = y - b / 200
+        [nx,ny,nz] = getZipList $ ((*) <$> ZipList ((transformXYZ) <$> [x,y,z])) <*> ZipList refWhite
+    in XYZ nx ny nz
+    
diff --git a/src/Data/Prizm/Color/Matrices/RGB.hs b/src/Data/Prizm/Color/Matrices/RGB.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Prizm/Color/Matrices/RGB.hs
@@ -0,0 +1,17 @@
+module Data.Prizm.Color.Matrices.RGB where
+
+import Data.Prizm.Types (RGBtoXYZ)
+
+-- http://www.brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html
+
+d65SRGB :: RGBtoXYZ
+d65SRGB =  [
+  [0.4124564, 0.3575761, 0.1804375],
+  [0.2126729, 0.7151522, 0.0721750],
+  [0.0193339, 0.1191920, 0.9503041]]
+
+d65Adobe :: RGBtoXYZ
+d65Adobe =  [
+  [0.5767309],[0.1855540],[0.1881852],
+  [0.2973769],[0.6273491],[0.0752741],
+  [0.0270343],[0.0706872],[0.9911085]]
diff --git a/src/Data/Prizm/Color/Matrices/XYZ.hs b/src/Data/Prizm/Color/Matrices/XYZ.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Prizm/Color/Matrices/XYZ.hs
@@ -0,0 +1,17 @@
+module Data.Prizm.Color.Matrices.XYZ where
+
+import Data.Prizm.Types (XYZtoRGB)
+
+-- http://www.brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html
+
+d65SRGB :: XYZtoRGB
+d65SRGB =  [
+  [3.2404542, (-1.5371385), (-0.4985314)],
+  [(-0.9692660), 1.8760108, 0.0415560],
+  [0.0556434, (-0.2040259), 1.0572252]]
+
+d65Adobe :: XYZtoRGB
+d65Adobe =  [
+  [2.0413690],[(-0.5649464)],[(-0.3446944)],
+  [(-0.9692660)],[1.8760108],[0.0415560],
+  [0.0134474],[(-0.1183897)],[1.0154096]]
diff --git a/src/Data/Prizm/Color/SRGB.hs b/src/Data/Prizm/Color/SRGB.hs
--- a/src/Data/Prizm/Color/SRGB.hs
+++ b/src/Data/Prizm/Color/SRGB.hs
@@ -1,30 +1,29 @@
 module Data.Prizm.Color.SRGB
 (
   toXYZ
+, toXYZMatrix
 ) where
 
 import Data.Prizm.Types
 import Data.Prizm.Color.Transform
+import Data.Prizm.Color.Matrices.RGB
 
 import Control.Applicative
 
-matrix :: [[Double]]
-matrix = [
-  [0.4124, 0.3576, 0.1805],
-  [0.2126, 0.7152, 0.0722],
-  [0.0193, 0.1192, 0.9505]]
-
 -- | @rgbTransform@ transform an RGB integer to be computed against
--- the rgbToXYZ matrix.
+-- a matrix.
 transform :: Integer -> Double
 transform v | dv > 0.04045 = (((dv + 0.055) / ap) ** 2.4) * 100
-               | otherwise    = (dv / 12.92) * 100
+            | otherwise    = (dv / 12.92) * 100
     where dv = fromIntegral v / 255
           ap = 1.0 + 0.055
 
 -- | @toXYZ@ convert an sRGB value to a CIE XYZ value.
-toXYZ :: SRGB -> CIE
-toXYZ (SRGB r g b) =
+toXYZ :: RGB -> CIE
+toXYZ = (toXYZMatrix d65SRGB)
+
+toXYZMatrix :: RGBtoXYZ -> RGB -> CIE
+toXYZMatrix m (RGB r g b) =
     let t = ZipList (transform <$> [r,g,b])
-        [x,y,z] = (zipTransform t) <$> matrix
+        [x,y,z] = (roundN 3) <$> ((zipTransform t) <$> m)
     in XYZ x y z
diff --git a/src/Data/Prizm/Color/Transform.hs b/src/Data/Prizm/Color/Transform.hs
--- a/src/Data/Prizm/Color/Transform.hs
+++ b/src/Data/Prizm/Color/Transform.hs
@@ -4,5 +4,11 @@
 
 import Control.Applicative
 
+roundN :: Integer -> Double -> Double
+roundN n num = (fromInteger $ round $ num * (10^n)) / (10.0^^n)
+
+truncateN :: Integer -> Double -> Double
+truncateN n num = (fromInteger $ truncate $ num * (10^n)) / (10.0^^n)
+
 zipTransform :: ZipList Double -> [Double] -> Double
 zipTransform tv m = sum $ getZipList $ (*) <$> ZipList m <*> tv
diff --git a/src/Data/Prizm/Types.hs b/src/Data/Prizm/Types.hs
--- a/src/Data/Prizm/Types.hs
+++ b/src/Data/Prizm/Types.hs
@@ -1,10 +1,13 @@
 module Data.Prizm.Types where
 
-data SRGB
-    = SRGB Integer Integer Integer
+type RGBtoXYZ = [[Double]]
+type XYZtoRGB = [[Double]]
+
+data RGB
+    = RGB Integer Integer Integer
     deriving (Eq, Ord, Show)
 
 data CIE
     = XYZ Double Double Double
---    | LAB Double Double Double
+    | LAB Double Double Double
     deriving (Eq, Ord, Show)
diff --git a/tests/QC.hs b/tests/QC.hs
new file mode 100644
--- /dev/null
+++ b/tests/QC.hs
@@ -0,0 +1,15 @@
+{-# OPTIONS_GHC -fno-warn-missing-signatures #-}
+
+module Main (main) where
+
+import qualified QC.SRGB as SRGB
+import qualified QC.CIE as CIE
+
+import Test.Framework (defaultMain, testGroup)
+
+main = defaultMain tests
+
+tests = [
+      testGroup "srgb" SRGB.tests
+    , testGroup "cie" CIE.tests
+      ]
diff --git a/tests/QC/SRGB.hs b/tests/QC/SRGB.hs
new file mode 100644
--- /dev/null
+++ b/tests/QC/SRGB.hs
@@ -0,0 +1,19 @@
+module QC.SRGB (tests) where
+
+import Test.Framework.Providers.QuickCheck2 (testProperty)
+import Test.QuickCheck
+
+import Control.Monad
+
+import Data.Prizm.Color.SRGB as S
+import Data.Prizm.Color.CIE as C
+import Data.Prizm.Types
+
+instance Arbitrary RGB where
+    arbitrary = liftM3 RGB (choose (0, 255)) (choose (0, 255)) (choose (0, 255))
+
+rgb2XYZ v = C.toRGB(S.toXYZ v) == v
+
+tests = [
+    testProperty "SRGB <-> CIE XYZ" rgb2XYZ
+      ]