diff --git a/ext/TensorKitChainRulesCoreExt.jl b/ext/TensorKitChainRulesCoreExt.jl
index 12d10509..47e8fb25 100644
--- a/ext/TensorKitChainRulesCoreExt.jl
+++ b/ext/TensorKitChainRulesCoreExt.jl
@@ -166,7 +166,7 @@ function ChainRulesCore.rrule(::typeof(TensorKit.tsvd!), t::AbstractTensorMap;
             Uc, Σc, Vc = block(U, c), block(Σ, c), block(V, c)
             ΔUc, ΔΣc, ΔVc = block(ΔU, c), block(ΔΣ, c), block(ΔV, c)
             Σdc = view(Σc, diagind(Σc))
-            ΔΣdc = view(ΔΣc, diagind(ΔΣc))
+            ΔΣdc = (ΔΣdc isa AbstractZero) ? ΔΣdc : view(ΔΣdc, diagind(ΔΣdc))
             copyto!(b, svd_pullback(Uc, Σdc, Vc, ΔUc, ΔΣdc, ΔVc))
         end
         return NoTangent(), Δt
diff --git a/src/tensors/truncation.jl b/src/tensors/truncation.jl
index f35efea2..61fe777d 100644
--- a/src/tensors/truncation.jl
+++ b/src/tensors/truncation.jl
@@ -164,8 +164,7 @@ function _truncate!(V::SectorVectorDict, trunc::TruncationSpace, p=2)
     end
     return V, truncerr
 end
-########################
-########################
+
 function _truncate!(V::SectorVectorDict, trunc::TruncationCutoff, p=2)
     I = keytype(V)
     S = real(eltype(valtype(V)))
diff --git a/test/ad.jl b/test/ad.jl
index 12e85970..a0060b3b 100644
--- a/test/ad.jl
+++ b/test/ad.jl
@@ -78,36 +78,14 @@ end
 # complex-valued svd?
 # -------------------
 
-# function _gaugefix!(U, V)
-#     s = LinearAlgebra.Diagonal(TensorKit._safesign.(diag(U)))
-#     rmul!(U, s)
-#     lmul!(s', V)
-#     return U, V
-# end
-
-# function _tsvd(t::AbstractTensorMap)
-#     U, S, V, ϵ = tsvd(t)
-#     for (c, b) in blocks(U)
-#         _gaugefix!(b, block(V, c))
-#     end
-#     return U, S, V, ϵ
-# end
-
-# svd_rev = Base.get_extension(TensorKit, :TensorKitChainRulesCoreExt).svd_rev
-
-# function ChainRulesCore.rrule(::typeof(_tsvd), t::AbstractTensorMap)
-#     U, S, V, ϵ = _tsvd(t)
-#     function _tsvd_pullback((ΔU, ΔS, ΔV, Δϵ))
-#         ∂t = similar(t)
-#         for (c, b) in blocks(∂t)
-#             copyto!(b,
-#                     svd_rev(block(U, c), block(S, c), block(V, c),
-#                             block(ΔU, c), block(ΔS, c), block(ΔV, c)))
-#         end
-#         return NoTangent(), ∂t
-#     end
-#     return (U, S, V, ϵ), _tsvd_pullback
-# end
+function remove_svdgauge_depence!(ΔU, ΔV, U, S, V)
+    # simple implementation, assumes no degeneracies or zeros in singular values
+    gaugepart = U' * ΔU + V * ΔV'
+    for (c, b) in blocks(gaugepart)
+        mul!(block(ΔU, c), block(U, c), Diagonal(imag(diag(b))), -im, 1)
+    end
+    return ΔU, ΔV
+end
 
 # Tests
 # -----
@@ -275,12 +253,7 @@ Vlist = ((ℂ^2, (ℂ^3)', ℂ^3, ℂ^2, (ℂ^2)'),
             ΔU = TensorMap(randn, scalartype(U), space(U))
             ΔS = TensorMap(randn, scalartype(S), space(S))
             ΔV = TensorMap(randn, scalartype(V), space(V))
-            if T <: Complex # remove gauge dependent components
-                gaugepart = U' * ΔU + V * ΔV'
-                for (c, b) in blocks(gaugepart)
-                    mul!(block(ΔU, c), block(U, c), Diagonal(imag(diag(b))), -im, 1)
-                end
-            end
+            T <: Complex && remove_svdgauge_depence!(ΔU, ΔV, U, S, V)
             test_rrule(tsvd, B; atol, output_tangent=(ΔU, ΔS, ΔV, 0.0))
 
             Vtrunc = spacetype(S)(TensorKit.SectorDict(c => ceil(Int, size(b, 1) / 2)
@@ -290,12 +263,7 @@ Vlist = ((ℂ^2, (ℂ^3)', ℂ^3, ℂ^2, (ℂ^2)'),
             ΔU = TensorMap(randn, scalartype(U), space(U))
             ΔS = TensorMap(randn, scalartype(S), space(S))
             ΔV = TensorMap(randn, scalartype(V), space(V))
-            if T <: Complex # remove gauge dependent components
-                gaugepart = U' * ΔU + V * ΔV'
-                for (c, b) in blocks(gaugepart)
-                    mul!(block(ΔU, c), block(U, c), Diagonal(imag(diag(b))), -im, 1)
-                end
-            end
+            T <: Complex && remove_svdgauge_depence!(ΔU, ΔV, U, S, V)
             test_rrule(tsvd, B; atol, output_tangent=(ΔU, ΔS, ΔV, 0.0),
                        fkwargs=(; trunc=truncspace(Vtrunc)))
         end
@@ -304,26 +272,17 @@ Vlist = ((ℂ^2, (ℂ^3)', ℂ^3, ℂ^2, (ℂ^2)'),
             ΔU = TensorMap(randn, scalartype(U), space(U))
             ΔS = TensorMap(randn, scalartype(S), space(S))
             ΔV = TensorMap(randn, scalartype(V), space(V))
-            if T <: Complex # remove gauge dependent components
-                gaugepart = U' * ΔU + V * ΔV'
-                for (c, b) in blocks(gaugepart)
-                    mul!(block(ΔU, c), block(U, c), Diagonal(imag(diag(b))), -im, 1)
-                end
-            end
+            T <: Complex && remove_svdgauge_depence!(ΔU, ΔV, U, S, V)
             test_rrule(tsvd, C; atol, output_tangent=(ΔU, ΔS, ΔV, 0.0))
 
-            U, S, V, ϵ = tsvd(C; trunc=truncdim(2))
+            c, = argmax(x -> sqrt(dim(x[1])) * maximum(diag(x[2])), blocks(S))
+            U, S, V, ϵ = tsvd(C; trunc=truncdim(2 * dim(c)))
             ΔU = TensorMap(randn, scalartype(U), space(U))
             ΔS = TensorMap(randn, scalartype(S), space(S))
             ΔV = TensorMap(randn, scalartype(V), space(V))
-            if T <: Complex # remove gauge dependent components
-                gaugepart = U' * ΔU + V * ΔV'
-                for (c, b) in blocks(gaugepart)
-                    mul!(block(ΔU, c), block(U, c), Diagonal(imag(diag(b))), -im, 1)
-                end
-            end
+            T <: Complex && remove_svdgauge_depence!(ΔU, ΔV, U, S, V)
             test_rrule(tsvd, C; atol, output_tangent=(ΔU, ΔS, ΔV, 0.0),
-                       fkwargs=(; trunc=truncdim(2)))
+                       fkwargs=(; trunc=truncdim(2 * dim(c))))
         end
     end
 end