diff --git a/Data/RangeSpace.hs b/Data/RangeSpace.hs
--- a/Data/RangeSpace.hs
+++ b/Data/RangeSpace.hs
@@ -1,7 +1,9 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE CPP #-}
 {-# LANGUAGE BangPatterns #-}
 {-# LANGUAGE DeriveFunctor #-}
 {-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE UndecidableInstances #-}
 
 ----------------------------------------------------------------------
 {- |
@@ -72,6 +74,7 @@
 
 import Control.Applicative
 import Control.Arrow             ((***))
+import Data.Semigroup
 import Data.List                 (zipWith4)
 
 #if MIN_VERSION_vector_space_points(0,1,2)
@@ -92,6 +95,9 @@
     pure a = Range a a
     (Range minf maxf) <*> (Range minv maxv) = Range (minf minv) (maxf maxv)
 
+instance (BasisRange t) => Semigroup (Range t) where
+    (<>) = unionRange
+
 -- | A '(minimum,maximum)' pair
 type Bounds t = (t,t)
 
@@ -152,21 +158,17 @@
 -- -------------------------------------------------------------------------
 -- multi-dimensional stuff
 
+-- | The necessary 'Constraint' for working with multi-dimensional ranges.
+type BasisRange t = (Ord t, AffineSpace t, HasBasis (Diff t)
+                    ,Ord (Scalar (Diff t)), Num (Scalar (Diff t)))
+
 -- | Create a range from a 'start,stop' pair.  For multi-dimensional ranges,
 -- the resulting range will be the union of the two points.
-newRange :: (Ord t, AffineSpace t, HasBasis (Diff t)
-            ,Ord (Scalar (Diff t)), Num (Scalar (Diff t)))
-         => t
-         -> t
-         -> Range t
+newRange :: BasisRange t => t -> t -> Range t
 newRange start stop = unionRange (Range start start) (Range stop stop)
 
 -- | Calculate the union of two 'Bounds'.  See the notes for @unionRange@.
-unionBounds :: (Num (Scalar (Diff t)), Ord (Scalar (Diff t)), Ord t,
-               HasBasis (Diff t), AffineSpace t)
-            => Bounds t
-            -> Bounds t
-            -> Bounds t
+unionBounds :: BasisRange t => Bounds t -> Bounds t -> Bounds t
 unionBounds r1 r2 = unRange $ unionRange (fromBounds r1) (fromBounds r2)
 
 -- | Calculate the union of two 'Range's, per-basis.
@@ -180,14 +182,12 @@
 -- doesn't require a full 'VectorSpace'. It does require that the
 -- affine space scalars are in a vector space, but this is more easily
 -- satisfiable.
-unionRange :: (Num (Scalar (Diff t)), Ord t, Ord (Scalar (Diff t)),
-                HasBasis (Diff t), AffineSpace t)
-           => Range t -> Range t -> Range t
+unionRange :: BasisRange t => Range t -> Range t -> Range t
 unionRange r0 r1 =
         Range (adjust combineMin min0 min1) (adjust combineMax max0 max1)
     where
-        combineMin diff = min diff 0
-        combineMax diff = max diff 0
+        combineMin dif = min dif 0
+        combineMax dif = max dif 0
         adjust f orig s = (orig .+^) . recompose . map (fmap f)
                              . decompose $ s .-. orig
         (min0,max0) = toBounds r0
@@ -199,8 +199,7 @@
 --  independently for each basis.
 --  If the range lies entirely outside the mask, the returned value
 --  is 'Range rmin rmin' (per-basis)
-maskRange :: (Eq (Basis (Diff t)), Num (Scalar (Diff t)), Ord t,
-                   Ord (Scalar (Diff t)), HasBasis (Diff t), AffineSpace t)
+maskRange :: (Eq (Basis (Diff t)), BasisRange t)
               => Range t    -- ^ restriction
               -> Range t    -- ^ original Range
               -> Range t
@@ -249,8 +248,7 @@
 -- -------------------------------------------------------------------------
 
 -- | True if a value lies inside a 'Range'.
-inRange :: (Ord a, AffineSpace a, HasBasis (Diff a), Eq (Basis (Diff a))
-           ,Num (Scalar (Diff a)) ,Ord (Scalar (Diff a)))
+inRange :: (BasisRange a, Eq (Basis (Diff a)))
         => a
         -> Range a
         -> Bool
diff --git a/range-space.cabal b/range-space.cabal
--- a/range-space.cabal
+++ b/range-space.cabal
@@ -2,7 +2,7 @@
 -- documentation, see http://haskell.org/cabal/users-guide/
 
 name:                range-space
-version:             0.1.0.4
+version:             0.1.1.0
 synopsis:            A Range type with vector-space instances
 description:         Provides functions for converting between ranges and spans
 homepage:            https://github.com/JohnLato/range-space
@@ -22,6 +22,7 @@
                        Data.RangeSpace.TwoD
   -- other-modules:       
   build-depends:       base >= 4.5 && < 5
+                      ,semigroups   >= 0.8 && < 0.10
                       ,vector-space == 0.8.*
                       ,vector-space-points == 0.1.*
   default-extensions: CPP
@@ -31,11 +32,12 @@
   type: exitcode-stdio-1.0
   main-is: Properties.hs
   hs-source-dirs: tests .
-  ghc-options:    -fhpc -hpcdir dist/hpc/mix/range-space-0.1.0.4
+  ghc-options:    -fhpc -hpcdir dist/hpc/mix/range-space-0.1.1.0
 
   build-depends:
       base,
       range-space,
+      semigroups,
       vector-space,
       vector-space-points,
       time                       == 1.4.*,