diff --git a/src/Adaptivity.jl b/src/Adaptivity.jl
index dc8b40e..c2caba0 100644
--- a/src/Adaptivity.jl
+++ b/src/Adaptivity.jl
@@ -539,6 +539,9 @@ function redistribute(
 end
 
 function get_cartesian_owners(gids,nparts,ncells)
+  # This is currently O(sqrt(np)), but I believe we could make it 
+  # O(ln(np)) if we ensured the search is sorted. Even faster if we sort 
+  # the gids first, which progressively reduces the number of ranges to search.
   ranges = map(nparts,ncells) do np, nc
     map(p -> PartitionedArrays.local_range(p,np,nc,false,false), 1:np)
   end
diff --git a/test/CartesianAdaptivityTests.jl b/test/CartesianAdaptivityTests.jl
index 70a046d..1921b50 100644
--- a/test/CartesianAdaptivityTests.jl
+++ b/test/CartesianAdaptivityTests.jl
@@ -121,7 +121,7 @@ end
 
 ############################################################################################
 
-function main(distribute)
+function main(distribute,ncells,isperiodic)
   fine_parts = (2,2)
   fine_ranks = distribute(LinearIndices((4,)))
 
@@ -130,7 +130,7 @@ function main(distribute)
 
   # Create models and glues
   if i_am_in(coarse_ranks)
-    parent = CartesianDiscreteModel(coarse_ranks,coarse_parts,(0,1,0,1),(4,4))
+    parent = CartesianDiscreteModel(coarse_ranks,coarse_parts,(0,1,0,1),ncells;isperiodic)
     child  = refine(parent,(2,2))
     coarse_adaptivity_glue = get_adaptivity_glue(child)
   else
@@ -153,4 +153,11 @@ function main(distribute)
   return
 end
 
+function main(distribute)
+  main(distribute,(8,8),(false,false))
+  main(distribute,(8,8),(true,false))
+  main(distribute,(4,4),(false,true))
+  main(distribute,(4,4),(true,true))
+end
+
 end # module AdaptivityTests
\ No newline at end of file