diff --git a/src/memorylayout.jl b/src/memorylayout.jl
index f7b9e46..4004c7d 100644
--- a/src/memorylayout.jl
+++ b/src/memorylayout.jl
@@ -645,6 +645,7 @@ gives an iterator containing the possible non-zero entries in the k-th row of A.
 """
 rowsupport(A, k) = rowsupport(MemoryLayout(A), A, k)
 rowsupport(A) = rowsupport(A, axes(A,1))
+rowsupport(A, k::CartesianIndex{2}) = rowsupport(A, k[1])
 
 colsupport(_, A, j) = axes(A,1)
 
@@ -656,6 +657,7 @@ gives an iterator containing the possible non-zero entries in the j-th column of
 """
 colsupport(A, j) = colsupport(MemoryLayout(A), A, j)
 colsupport(A) = colsupport(A, axes(A,2))
+colsupport(A, k::CartesianIndex{2}) = rowsupport(A, k[2])
 
 # TODO: generalise to other subarrays
 function colsupport(A::SubArray{<:Any,N,<:Any,<:Tuple{Slice,AbstractVector}}, j) where N
diff --git a/test/test_layouts.jl b/test/test_layouts.jl
index 19e186b..64ddd06 100644
--- a/test/test_layouts.jl
+++ b/test/test_layouts.jl
@@ -134,7 +134,7 @@ struct FooNumber <: Number end
                 subdiagonaldata(Bl) == supdiagonaldata(Adjoint(Bl)) == supdiagonaldata(Transpose(Bl)) ==
                 T.dl
 
-        @test colsupport(T,3) == rowsupport(T,3) == colsupport(S,3) == rowsupport(S,3) == 2:4
+        @test colsupport(T,3) == rowsupport(T,3) == colsupport(S,3) == rowsupport(S,3) == rowsupport(T,CartesianIndex(3,2)) == colsupport(T,CartesianIndex(2,3)) == 2:4
         @test colsupport(T,3:6) == rowsupport(T,3:6) == colsupport(S,3:6) == rowsupport(S,3:6) == 2:6
         @test colsupport(Bl,3) == rowsupport(Bu,3) == rowsupport(Adjoint(Bl),3) == 3:4
         @test rowsupport(Bl,3) == colsupport(Bu,3) == colsupport(Adjoint(Bl),3) == 2:3