diff --git a/test/manellic/testManellicTree.jl b/test/manellic/testManellicTree.jl
index 175f54d..3675ae2 100755
--- a/test/manellic/testManellicTree.jl
+++ b/test/manellic/testManellicTree.jl
@@ -869,12 +869,14 @@ end
 
 @show best_cov = abs.(Optim.minimizer(res))
 
-@test isapprox([0.6; 0.6; 0.06], best_cov; atol=0.35)
+@test isapprox([0.6; 0.6], best_cov[1:2]; atol=0.35)
+@test isapprox(0.06, best_cov[3]; atol=0.04)
 
 
 mkd = ApproxManifoldProducts.manikde!_manellic(M,pts)
 
-@test isapprox([0.6 0 0; 0 0.6 0; 0 0 0.06], getBW(mkd)[1]; atol=0.35)
+@test isapprox([0.6 0; 0 0.6], getBW(mkd)[1][1:2,1:2]; atol=0.35)
+@test isapprox(0.06, getBW(mkd)[1][3,3]; atol=0.04)
 
 
 ##
@@ -882,6 +884,42 @@ end
 
 
 
+@testset "Multidimensional LOOCV bandwidth optimization, SpecialEuclidean(3)" begin
+##
+
+M = SpecialEuclidean(3)
+pts = [ArrayPartition(SA[randn(3)...;],SMatrix{3,3,Float64}(collect(Rot_.RotXYZ(0.1*randn(3)...)))) for _ in 1:64]
+
+bw = SA[1.0; 1.0; 1.0; 0.3; 0.3; 0.3]
+mtree = ApproxManifoldProducts.buildTree_Manellic!(M, pts; kernel_bw=bw,kernel=AMP.MvNormalKernel)
+
+cost4(σ) = begin
+  AMP.entropy(mtree, diagm(σ.^2))
+end
+
+# and optimize with "update" kernel bandwith cost
+@time res = Optim.optimize(
+  cost4, 
+  collect(bw), 
+  Optim.NelderMead()
+);
+
+@test res.ls_success
+
+@show best_cov = abs.(Optim.minimizer(res))
+
+@test isapprox([0.75; 0.75; 0.75], best_cov[1:3]; atol=0.4)
+@test isapprox([0.06; 0.06; 0.06], best_cov[4:6]; atol=0.04)
+
+
+mkd = ApproxManifoldProducts.manikde!_manellic(M,pts)
+
+@test isapprox([0.75 0 0; 0 0.75 0; 0 0 0.75], getBW(mkd)[1][1:3,1:3]; atol=0.4)
+@test isapprox([0.06 0 0; 0 0.06 0; 0 0 0.06], getBW(mkd)[1][4:6,4:6]; atol=0.04)
+
+##
+end
+
 ##
 # # using GLMakie
 
@@ -1064,4 +1102,4 @@ end
 # lines!((s->s[1]).(XX),YY, color=:red)
 
 
-#
\ No newline at end of file
+#