diff --git a/test/toeplitzplanstests.jl b/test/toeplitzplanstests.jl
index 46b13f98..6ea6a095 100644
--- a/test/toeplitzplanstests.jl
+++ b/test/toeplitzplanstests.jl
@@ -54,12 +54,66 @@ import FastTransforms: plan_uppertoeplitz!
                 @test PX[:,j,:] ≈ X[:,j,:]*T'
             end
 
+            P = plan_uppertoeplitz!([1,2,3], size(X), (1,3))
+            PX = P * copy(X)
+            for j = 1:size(X,2)
+                @test PX[:,j,:] ≈ T*X[:,j,:]*T'
+            end
+
+            P = plan_uppertoeplitz!([1,2,3], size(X), 1:3)
+            PX = P * copy(X)
+            M = copy(X)
+            for j = 1:size(X,3)
+                M[:,:,j] = T*M[:,:,j]*T'
+            end
+            for k = 1:size(X,1)
+                M[k,:,:] = M[k,:,:]*T'
+            end
+            @test M ≈ PX
+        end
 
-            # P = plan_uppertoeplitz!([1,2,3], size(X), 1:3)
-            # PX = P * copy(X)
-            # for j = 1:size(X,2)
-            #     @test PX[:,j,:] ≈ X[:,j,:]*T'
-            # end
+        @testset "4D" begin
+            X = randn(3,3,3,3)
+            P = plan_uppertoeplitz!([1,2,3], size(X), 1)
+            PX = P * copy(X)
+            for ℓ = 1:size(X,3), m = 1:size(X,4)
+                @test PX[:,:,ℓ,m] ≈ T*X[:,:,ℓ,m]
+            end
+
+            P = plan_uppertoeplitz!([1,2,3], size(X), 2)
+            PX = P * copy(X)
+            for ℓ = 1:size(X,3), m = 1:size(X,4)
+                @test PX[:,:,ℓ,m] ≈ X[:,:,ℓ,m]*T'
+            end
+
+            P = plan_uppertoeplitz!([1,2,3], size(X), 3)
+            PX = P * copy(X)
+            for j = 1:size(X,2), m = 1:size(X,4)
+                @test PX[:,j,:,m] ≈ X[:,j,:,m]*T'
+            end
+
+            P = plan_uppertoeplitz!([1,2,3], size(X), 4)
+            PX = P * copy(X)
+            for k = 1:size(X,1), j = 1:size(X,2)
+                @test PX[k,j,:,:] ≈ X[k,j,:,:]*T'
+            end
+
+            P = plan_uppertoeplitz!([1,2,3], size(X), (1,3))
+            PX = P * copy(X)
+            for j = 1:size(X,2), m=1:size(X,4)
+                @test PX[:,j,:,m] ≈ T*X[:,j,:,m]*T'
+            end
+
+            P = plan_uppertoeplitz!([1,2,3], size(X), 1:4)
+            PX = P * copy(X)
+            M = copy(X)
+            for ℓ = 1:size(X,3), m = 1:size(X,4)
+                M[:,:,ℓ,m] = T*M[:,:,ℓ,m]*T'
+            end
+            for k = 1:size(X,1), j = 1:size(X,2)
+                M[k,j,:,:] = T*M[k,j,:,:]*T'
+            end
+            @test M ≈ PX
         end
     end