diff --git a/grid.cabal b/grid.cabal
--- a/grid.cabal
+++ b/grid.cabal
@@ -1,5 +1,5 @@
 name:           grid
-version:        7.5
+version:        7.6
 synopsis:       Tools for working with regular grids (graphs, lattices).
 description:    Provides tools for working with regular arrangements
                 of tiles, such as might be used in a board game or some
@@ -22,7 +22,7 @@
   hs-source-dirs:  src
   build-depends:   base ==4.*,
                    base-unicode-symbols ==0.2.*,
-                   cereal ==0.4.*,
+                   cereal ==0.3.* || ==0.4.*,
                    containers ==0.4.2.* || ==0.5.*
   ghc-options:     -Wall
   exposed-modules: Math.Geometry.Grid,
diff --git a/src/Math/Geometry/GridInternal.hs b/src/Math/Geometry/GridInternal.hs
--- a/src/Math/Geometry/GridInternal.hs
+++ b/src/Math/Geometry/GridInternal.hs
@@ -18,7 +18,7 @@
 import Prelude hiding (null)
 
 import Data.Function (on)
-import Data.List (groupBy, nub, nubBy, sortBy)
+import Data.List ((\\), groupBy, nub, nubBy, sortBy)
 import Data.Ord (comparing)
 
 -- | A regular arrangement of tiles.
@@ -52,6 +52,12 @@
   neighbours :: Eq (Index g) => g -> Index g -> [Index g]
   neighbours = defaultNeighbours
 
+  -- | @'neighboursOfSet' g as@ returns the indices of the tiles in the
+  --   grid @g@ which are adjacent to any of the tiles with index in
+  --   @as@.
+  neighboursOfSet :: Eq (Index g) => g -> [Index g] -> [Index g]
+  neighboursOfSet = defaultNeighboursOfSet
+
   -- | @'neighbour' g d a@ returns the indices of the tile in the grid
   --   @g@ which is adjacent to the tile with index @a@, in the
   --   direction @d@.
@@ -142,6 +148,11 @@
   -- WARNING: this implementation won't work for wrapped grids
   defaultNeighbours :: g -> Index g -> [Index g]
   defaultNeighbours g a = filter (\b -> distance g a b == 1 ) $ indices g
+
+  -- This should work for wrapped grids, though.
+  defaultNeighboursOfSet :: Eq (Index g) => g -> [Index g] -> [Index g]
+  defaultNeighboursOfSet g as = ns \\ as
+    where ns = nub . concatMap (neighbours g) $ as
 
   -- WARNING: this implementation won't work for wrapped grids
   defaultNeighbour :: (Eq (Index g), Eq (Direction g))
diff --git a/test/Math/Geometry/GridQC.hs b/test/Math/Geometry/GridQC.hs
--- a/test/Math/Geometry/GridQC.hs
+++ b/test/Math/Geometry/GridQC.hs
@@ -186,6 +186,22 @@
   where g = grid t
         (a:b:_) = points t
 
+prop_custom_neighboursOfSet_eq_default
+  :: (TestData t, Grid (BaseGrid t), Ord (Index (BaseGrid t)))
+    => t -> Property
+prop_custom_neighboursOfSet_eq_default t = nonNull g ==>
+  neighboursOfSet g as == defaultNeighboursOfSet g as
+  where g = grid t
+        as = points t
+
+prop_custom_neighboursOfSet_cw_minDistance
+  :: (TestData t, Grid (BaseGrid t), Ord (Index (BaseGrid t)))
+    => t -> Property
+prop_custom_neighboursOfSet_cw_minDistance t = nonNull g ==>
+  a `elem` (neighboursOfSet g bs) || minDistance g bs a /= 1 
+  where g = grid t
+        (a:bs) = points t
+
 gridProperties 
   :: (TestData t, Grid (BaseGrid t), Arbitrary t, 
     Eq (Index (BaseGrid t)), Ord (Index (BaseGrid t)), 
@@ -204,7 +220,9 @@
     ("prop_minimal_paths_have_min_length: " ++ s, prop_minimal_paths_have_min_length),
     ("prop_minimal_paths_are_valid: " ++ s, prop_minimal_paths_are_valid),
     ("prop_neighbour_cw_directionTo: " ++ s, prop_neighbour_cw_directionTo),
-    ("prop_custom_adjacentTilesToward_eq_default: " ++ s, prop_custom_adjacentTilesToward_eq_default)
+    ("prop_custom_adjacentTilesToward_eq_default: " ++ s, prop_custom_adjacentTilesToward_eq_default),
+    ("prop_custom_neighboursOfSet_eq_default: " ++ s, prop_custom_neighboursOfSet_eq_default),
+    ("prop_custom_neighboursOfSet_cw_minDistance: " ++ s, prop_custom_neighboursOfSet_cw_minDistance)
   ]
 
 --