diff --git a/NDTensors/Project.toml b/NDTensors/Project.toml
index e25bea22a2..4c992ae743 100644
--- a/NDTensors/Project.toml
+++ b/NDTensors/Project.toml
@@ -1,7 +1,7 @@
 name = "NDTensors"
 uuid = "23ae76d9-e61a-49c4-8f12-3f1a16adf9cf"
 authors = ["Matthew Fishman <mfishman@flatironinstitute.org>"]
-version = "0.3.12"
+version = "0.3.13"
 
 [deps]
 Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
diff --git a/NDTensors/src/lib/TensorAlgebra/src/blockedpermutation.jl b/NDTensors/src/lib/TensorAlgebra/src/blockedpermutation.jl
index 160cd3aec8..c13b68a642 100644
--- a/NDTensors/src/lib/TensorAlgebra/src/blockedpermutation.jl
+++ b/NDTensors/src/lib/TensorAlgebra/src/blockedpermutation.jl
@@ -160,9 +160,7 @@ end
 
 BlockArrays.blocks(blockedperm::BlockedPermutation) = getfield(blockedperm, :blocks)
 
-function blockedperm(length::Val, permblocks_maybe_empty::Tuple{Vararg{Int}}...)
-  # Drop empty blocks
-  permblocks = filter(!isempty, permblocks_maybe_empty)
+function blockedperm(length::Val, permblocks::Tuple{Vararg{Int}}...)
   @assert value(length) == sum(Base.length, permblocks; init=zero(Bool))
   blockedperm = _BlockedPermutation(permblocks)
   @assert isperm(blockedperm)
diff --git a/NDTensors/src/lib/TensorAlgebra/src/contract/allocate_output.jl b/NDTensors/src/lib/TensorAlgebra/src/contract/allocate_output.jl
index 7732fa1258..2beff4c5bc 100644
--- a/NDTensors/src/lib/TensorAlgebra/src/contract/allocate_output.jl
+++ b/NDTensors/src/lib/TensorAlgebra/src/contract/allocate_output.jl
@@ -30,11 +30,43 @@ function output_axes(
   α::Number=true,
 )
   axes_contracted = blockpermute(axes(a1), perm1)
-  axes_contracted2 = blockpermute(axes(a2), perm2)
-  @assert axes_contracted == axes_contracted2
+  axes_contracted′ = blockpermute(axes(a2), perm2)
+  @assert axes_contracted == axes_contracted′
   return ()
 end
 
+# Vec-mat.
+function output_axes(
+  ::typeof(contract),
+  perm_dest::BlockedPermutation{1},
+  a1::AbstractArray,
+  perm1::BlockedPermutation{1},
+  a2::AbstractArray,
+  biperm2::BlockedPermutation{2},
+  α::Number=true,
+)
+  (axes_contracted,) = blockpermute(axes(a1), perm1)
+  axes_contracted′, axes_dest = blockpermute(axes(a2), biperm2)
+  @assert axes_contracted == axes_contracted′
+  return genperm((axes_dest...,), invperm(Tuple(perm_dest)))
+end
+
+# Mat-vec.
+function output_axes(
+  ::typeof(contract),
+  perm_dest::BlockedPermutation{1},
+  a1::AbstractArray,
+  perm1::BlockedPermutation{2},
+  a2::AbstractArray,
+  biperm2::BlockedPermutation{1},
+  α::Number=true,
+)
+  axes_dest, axes_contracted = blockpermute(axes(a1), perm1)
+  (axes_contracted′,) = blockpermute(axes(a2), biperm2)
+  @assert axes_contracted == axes_contracted′
+  return genperm((axes_dest...,), invperm(Tuple(perm_dest)))
+end
+
 # TODO: Use `ArrayLayouts`-like `MulAdd` object,
 # i.e. `ContractAdd`?
 function allocate_output(
diff --git a/NDTensors/src/lib/TensorAlgebra/src/contract/blockedperms.jl b/NDTensors/src/lib/TensorAlgebra/src/contract/blockedperms.jl
index 22d103c293..60009de9ef 100644
--- a/NDTensors/src/lib/TensorAlgebra/src/contract/blockedperms.jl
+++ b/NDTensors/src/lib/TensorAlgebra/src/contract/blockedperms.jl
@@ -22,8 +22,11 @@ function blockedperms(::typeof(contract), dimnames_dest, dimnames1, dimnames2)
   perm_codomain2 = BaseExtensions.indexin(contracted, dimnames2)
   perm_domain2 = BaseExtensions.indexin(domain, dimnames2)
 
-  biperm_dest = blockedperm(perm_codomain_dest, perm_domain_dest)
-  biperm1 = blockedperm(perm_codomain1, perm_domain1)
-  biperm2 = blockedperm(perm_codomain2, perm_domain2)
+  permblocks_dest = (perm_codomain_dest, perm_domain_dest)
+  biperm_dest = blockedperm(filter(!isempty, permblocks_dest)...)
+  permblocks1 = (perm_codomain1, perm_domain1)
+  biperm1 = blockedperm(filter(!isempty, permblocks1)...)
+  permblocks2 = (perm_codomain2, perm_domain2)
+  biperm2 = blockedperm(filter(!isempty, permblocks2)...)
   return biperm_dest, biperm1, biperm2
 end
diff --git a/NDTensors/src/lib/TensorAlgebra/src/contract/contract_matricize/contract.jl b/NDTensors/src/lib/TensorAlgebra/src/contract/contract_matricize/contract.jl
index 3ddc38ff76..beb70104bb 100644
--- a/NDTensors/src/lib/TensorAlgebra/src/contract/contract_matricize/contract.jl
+++ b/NDTensors/src/lib/TensorAlgebra/src/contract/contract_matricize/contract.jl
@@ -39,3 +39,19 @@ function _mul!(
   a_dest[] = transpose(a1) * a2 * α + a_dest[] * β
   return a_dest
 end
+
+# Vec-mat.
+function _mul!(
+  a_dest::AbstractVector, a1::AbstractVector, a2::AbstractMatrix, α::Number, β::Number
+)
+  mul!(transpose(a_dest), transpose(a1), a2, α, β)
+  return a_dest
+end
+
+# Mat-vec.
+function _mul!(
+  a_dest::AbstractVector, a1::AbstractMatrix, a2::AbstractVector, α::Number, β::Number
+)
+  mul!(a_dest, a1, a2, α, β)
+  return a_dest
+end
diff --git a/NDTensors/src/lib/TensorAlgebra/test/test_basics.jl b/NDTensors/src/lib/TensorAlgebra/test/test_basics.jl
index 40eefecc8b..22feb8c2aa 100644
--- a/NDTensors/src/lib/TensorAlgebra/test/test_basics.jl
+++ b/NDTensors/src/lib/TensorAlgebra/test/test_basics.jl
@@ -22,6 +22,18 @@ const elts = (Float32, Float64, Complex{Float32}, Complex{Float64})
   @test blocklasts(p) == (3, 5)
   @test invperm(p) == blockedperm((5, 4, 1), (2, 3))
 
+  # Empty block.
+  p = blockedperm((3, 2), (), (1,))
+  @test Tuple(p) === (3, 2, 1)
+  @test isperm(p)
+  @test length(p) == 3
+  @test blocks(p) == ((3, 2), (), (1,))
+  @test blocklength(p) == 3
+  @test blocklengths(p) == (2, 0, 1)
+  @test blockfirsts(p) == (1, 3, 3)
+  @test blocklasts(p) == (2, 2, 3)
+  @test invperm(p) == blockedperm((3, 2), (), (1,))
+
   # Split collection into `BlockedPermutation`.
   p = blockedperm_indexin(("a", "b", "c", "d"), ("c", "a"), ("b", "d"))
   @test p == blockedperm((3, 1), (2, 4))
@@ -120,6 +132,8 @@ end
       for (d1s, d2s, d_dests) in (
         ((1, 2), (1, 2), ()),
         ((1, 2), (2, 1), ()),
+        ((1, 2), (2, 1, 3), (3,)),
+        ((1, 2, 3), (2, 1), (3,)),
         ((1, 2), (2, 3), (1, 3)),
         ((1, 2), (2, 3), (3, 1)),
         ((2, 1), (2, 3), (3, 1)),