diff --git a/src/caches/beliefpropagationcache.jl b/src/caches/beliefpropagationcache.jl
index 1f465fd9..3b77a0b1 100644
--- a/src/caches/beliefpropagationcache.jl
+++ b/src/caches/beliefpropagationcache.jl
@@ -32,20 +32,14 @@ default_partitioned_vertices(ψ::AbstractITensorNetwork) = group(v -> v, vertice
 function default_partitioned_vertices(f::AbstractFormNetwork)
   return group(v -> original_state_vertex(f, v), vertices(f))
 end
-default_cache_update_kwargs(cache) = (; maxiter=20, tol=1e-5)
+default_cache_update_kwargs(cache) = (; maxiter=25, tol=1e-8)
 function default_cache_construction_kwargs(alg::Algorithm"bp", ψ::AbstractITensorNetwork)
   return (; partitioned_vertices=default_partitioned_vertices(ψ))
 end
 
 function message_diff(message_a::Vector{ITensor}, message_b::Vector{ITensor})
   lhs, rhs = contract(message_a), contract(message_b)
-  @assert issetequal(inds(lhs), inds(rhs))
-  c = combiner(inds(lhs))
-  lhs *= c
-  rhs *= c
-  lhs /= norm(lhs)
-  rhs /= norm(rhs)
-  f = abs(dot(lhs, rhs))^2
+  f = abs(dot(lhs / norm(lhs), rhs / norm(rhs)))^2
   return 1 - f
 end
 
diff --git a/test/test_gauging.jl b/test/test_gauging.jl
index 9eb4ebbf..67b1b5dd 100644
--- a/test/test_gauging.jl
+++ b/test/test_gauging.jl
@@ -27,9 +27,7 @@ using Test: @test, @testset
   ψ = random_tensornetwork(rng, s; link_space=χ)
 
   # Move directly to vidal gauge
-  ψ_vidal = VidalITensorNetwork(
-    ψ; cache_update_kwargs=(; maxiter=20, tol=1e-12, verbose=true)
-  )
+  ψ_vidal = VidalITensorNetwork(ψ; cache_update_kwargs=(; maxiter=30, verbose=true))
   @test gauge_error(ψ_vidal) < 1e-8
 
   # Move to symmetric gauge
@@ -38,7 +36,7 @@ using Test: @test, @testset
   bp_cache = cache_ref[]
 
   # Test we just did a gauge transform and didn't change the overall network
-  @test inner(ψ_symm, ψ) / sqrt(inner(ψ_symm, ψ_symm) * inner(ψ, ψ)) ≈ 1.0
+  @test inner(ψ_symm, ψ) / sqrt(inner(ψ_symm, ψ_symm) * inner(ψ, ψ)) ≈ 1.0 atol = 1e-8
 
   #Test all message tensors are approximately diagonal even when we keep running BP
   bp_cache = update(bp_cache; maxiter=10)