diff --git a/src/mapreduce.jl b/src/mapreduce.jl
index 245983e..be6dfa4 100644
--- a/src/mapreduce.jl
+++ b/src/mapreduce.jl
@@ -47,3 +47,14 @@ macro implement_mapreduce(t)
         end
     end
 end
+
+
+# optimized implementation for special cases
+
+for fname in [:sum,:prod,:count,:all,:any,:minimum,:maximum]
+    @eval function Base.$fname(v::AbstractDiskArray)
+        $fname(eachchunk(v)) do chunk
+            $fname(v[chunk...])
+        end
+    end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 49cbc1c..bfd8fef 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -907,10 +907,23 @@ end
     @test getindex_count(A) == 0 
 end
 
+@testset "optimization for associative reductions" begin
+    A = rand(1:10,30,30)
+    DA = AccessCountDiskArray(A,chunksize=(2,2))
 
+    for fun in (sum, prod, maximum, minimum)
+        @test fun(A) == fun(DA)
+    end
+
+    Ab = rand(Bool,30,30)
+    DAb = AccessCountDiskArray(Ab,chunksize=(2,2))
+    for fun in (count, all, any)
+        @test fun(Ab) == fun(DAb)
+    end
+end
 
 # @test offsets    == [[1:1,2:3,4:4],[5:5,6:6,7:7],[8:8,9:9]]
 # inds = [1,1,1,3,5,6,6,7,10,13,16,16,19,20]
 # readranges, offsets = find_subranges_sorted(inds,false)
 # @test readranges == [1:1, 3:3, 5:7, 10:10, 13:13, 16:16, 19:20]
-# @test offsets == [[1:3], [4:4], [5:5,6:7,8:8], [9:9], [10:10], [11:12], [13:13,14:14]]
\ No newline at end of file
+# @test offsets == [[1:3], [4:4], [5:5,6:7,8:8], [9:9], [10:10], [11:12], [13:13,14:14]]