diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,7 @@
+1.14
+----
+* Moved `Coincides` to `Linear.Plucker.Coincides`. The constructors `Line` and `Ray` oft collided with user code.
+
 1.13
 ----
 * Switched 'ortho' to follow the OpenGL handedness.
diff --git a/linear.cabal b/linear.cabal
--- a/linear.cabal
+++ b/linear.cabal
@@ -1,6 +1,6 @@
 name:          linear
 category:      Math, Algebra
-version:       1.13
+version:       1.14
 license:       BSD3
 cabal-version: >= 1.8
 license-file:  LICENSE
@@ -61,6 +61,7 @@
     Linear.Metric
     Linear.Perspective
     Linear.Plucker
+    Linear.Plucker.Coincides
     Linear.Quaternion
     Linear.Trace
     Linear.V
diff --git a/src/Linear/Plucker.hs b/src/Linear/Plucker.hs
--- a/src/Linear/Plucker.hs
+++ b/src/Linear/Plucker.hs
@@ -34,7 +34,8 @@
   , quadranceToOrigin
   , closestToOrigin
   , isLine
-  , Coincides(..)
+  , coincides
+  , coincides'
   -- * Basis elements
   ,      p01, p02, p03
   , p10,      p12, p13
@@ -442,26 +443,6 @@
         saveDiv x y | nearZero y = Option Nothing
                     | otherwise  = Option . Just $ First (x / y)
 {-# INLINABLE coincides' #-}
-
--- | When lines are represented as Plücker coordinates, we have the
--- ability to check for both directed and undirected
--- equality. Undirected equality between 'Line's (or a 'Line' and a
--- 'Ray') checks that the two lines coincide in 3D space. Directed
--- equality, between two 'Ray's, checks that two lines coincide in 3D,
--- and have the same direction. To accomodate these two notions of
--- equality, we use an 'Eq' instance on the 'Coincides' data type.
---
--- For example, to check the /directed/ equality between two lines,
--- @p1@ and @p2@, we write, @Ray p1 == Ray p2@.
-data Coincides a where
-  Line :: (Epsilon a, Fractional a) => Plucker a -> Coincides a
-  Ray  :: (Epsilon a, Fractional a, Ord a) => Plucker a -> Coincides a
-
-instance Eq (Coincides a) where
-  Line a == Line b  = coincides a b
-  Line a == Ray b   = coincides a b
-  Ray a  == Line b  = coincides a b
-  Ray a  == Ray b   = coincides' a b
 
 -- | The minimum squared distance of a line from the origin.
 quadranceToOrigin :: Fractional a => Plucker a -> a
diff --git a/src/Linear/Plucker/Coincides.hs b/src/Linear/Plucker/Coincides.hs
new file mode 100644
--- /dev/null
+++ b/src/Linear/Plucker/Coincides.hs
@@ -0,0 +1,38 @@
+{-# LANGUAGE GADTs #-}
+---------------------------------------------------------------------------------
+-- |
+-- Copyright   :  (C) 2012-2014 Edward Kmett,
+-- License     :  BSD-style (see the file LICENSE)
+--
+-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
+-- Stability   :  experimental
+-- Portability :  non-portable
+--
+-- Utility for working with Plücker coordinates for lines in 3d homogeneous space.
+----------------------------------------------------------------------------------
+module Linear.Plucker.Coincides
+  ( Coincides(..)
+  ) where
+
+import Linear.Epsilon
+import Linear.Plucker
+
+-- | When lines are represented as Plücker coordinates, we have the
+-- ability to check for both directed and undirected
+-- equality. Undirected equality between 'Line's (or a 'Line' and a
+-- 'Ray') checks that the two lines coincide in 3D space. Directed
+-- equality, between two 'Ray's, checks that two lines coincide in 3D,
+-- and have the same direction. To accomodate these two notions of
+-- equality, we use an 'Eq' instance on the 'Coincides' data type.
+--
+-- For example, to check the /directed/ equality between two lines,
+-- @p1@ and @p2@, we write, @Ray p1 == Ray p2@.
+data Coincides a where
+  Line :: (Epsilon a, Fractional a) => Plucker a -> Coincides a
+  Ray  :: (Epsilon a, Fractional a, Ord a) => Plucker a -> Coincides a
+
+instance Eq (Coincides a) where
+  Line a == Line b  = coincides a b
+  Line a == Ray b   = coincides a b
+  Ray a  == Line b  = coincides a b
+  Ray a  == Ray b   = coincides' a b