diff --git a/NDTensors/src/lib/TypeParameterAccessors/src/TypeParameterAccessors.jl b/NDTensors/src/lib/TypeParameterAccessors/src/TypeParameterAccessors.jl
index adafed6567..3333cd417b 100644
--- a/NDTensors/src/lib/TypeParameterAccessors/src/TypeParameterAccessors.jl
+++ b/NDTensors/src/lib/TypeParameterAccessors/src/TypeParameterAccessors.jl
@@ -12,6 +12,7 @@ include("unspecify_parameters.jl")
 include("set_parameters.jl")
 include("specify_parameters.jl")
 include("default_parameters.jl")
+include("ndims.jl")
 include("base/abstractarray.jl")
 include("base/similartype.jl")
 include("base/array.jl")
diff --git a/NDTensors/src/lib/TypeParameterAccessors/src/base/abstractarray.jl b/NDTensors/src/lib/TypeParameterAccessors/src/base/abstractarray.jl
index 14286b65cb..89e38d3b2f 100644
--- a/NDTensors/src/lib/TypeParameterAccessors/src/base/abstractarray.jl
+++ b/NDTensors/src/lib/TypeParameterAccessors/src/base/abstractarray.jl
@@ -13,6 +13,9 @@ end
 function set_ndims(type::Type{<:AbstractArray}, param)
   return set_type_parameter(type, ndims, param)
 end
+function set_ndims(type::Type{<:AbstractArray}, param::NDims)
+  return set_type_parameter(type, ndims, ndims(param))
+end
 
 using SimpleTraits: SimpleTraits, @traitdef, @traitimpl
 
diff --git a/NDTensors/src/lib/TypeParameterAccessors/src/base/similartype.jl b/NDTensors/src/lib/TypeParameterAccessors/src/base/similartype.jl
index c51bf80b6e..f6fed09885 100644
--- a/NDTensors/src/lib/TypeParameterAccessors/src/base/similartype.jl
+++ b/NDTensors/src/lib/TypeParameterAccessors/src/base/similartype.jl
@@ -5,13 +5,23 @@ like `OffsetArrays` or named indices
 (such as ITensors).
 """
 function set_indstype(arraytype::Type{<:AbstractArray}, dims::Tuple)
-  return set_ndims(arraytype, length(dims))
+  return set_ndims(arraytype, NDims(length(dims)))
+end
+
+function similartype(arraytype::Type{<:AbstractArray}, eltype::Type, ndims::NDims)
+  return similartype(similartype(arraytype, eltype), ndims)
 end
 
 function similartype(arraytype::Type{<:AbstractArray}, eltype::Type, dims::Tuple)
   return similartype(similartype(arraytype, eltype), dims)
 end
 
+@traitfn function similartype(
+  arraytype::Type{ArrayT}
+) where {ArrayT; !IsWrappedArray{ArrayT}}
+  return arraytype
+end
+
 @traitfn function similartype(
   arraytype::Type{ArrayT}, eltype::Type
 ) where {ArrayT; !IsWrappedArray{ArrayT}}
@@ -24,19 +34,29 @@ end
   return set_indstype(arraytype, dims)
 end
 
-function similartype(arraytype::Type{<:AbstractArray}, dims::Base.DimOrInd...)
-  return similartype(arraytype, dims)
+@traitfn function similartype(
+  arraytype::Type{ArrayT}, ndims::NDims
+) where {ArrayT; !IsWrappedArray{ArrayT}}
+  return set_ndims(arraytype, ndims)
 end
 
-function similartype(arraytype::Type{<:AbstractArray})
-  return similartype(arraytype, eltype(arraytype))
+function similartype(
+  arraytype::Type{<:AbstractArray}, dim1::Base.DimOrInd, dim_rest::Base.DimOrInd...
+)
+  return similartype(arraytype, (dim1, dim_rest...))
 end
 
 ## Wrapped arrays
+@traitfn function similartype(
+  arraytype::Type{ArrayT}
+) where {ArrayT; IsWrappedArray{ArrayT}}
+  return similartype(unwrap_array_type(arraytype), NDims(arraytype))
+end
+
 @traitfn function similartype(
   arraytype::Type{ArrayT}, eltype::Type
 ) where {ArrayT; IsWrappedArray{ArrayT}}
-  return similartype(unwrap_array_type(arraytype), eltype)
+  return similartype(unwrap_array_type(arraytype), eltype, NDims(arraytype))
 end
 
 @traitfn function similartype(
@@ -45,6 +65,12 @@ end
   return similartype(unwrap_array_type(arraytype), dims)
 end
 
+@traitfn function similartype(
+  arraytype::Type{ArrayT}, ndims::NDims
+) where {ArrayT; IsWrappedArray{ArrayT}}
+  return similartype(unwrap_array_type(arraytype), ndims)
+end
+
 # This is for uniform `Diag` storage which uses
 # a Number as the data type.
 # TODO: Delete this when we change to using a
diff --git a/NDTensors/src/lib/TypeParameterAccessors/src/ndims.jl b/NDTensors/src/lib/TypeParameterAccessors/src/ndims.jl
new file mode 100644
index 0000000000..f640763583
--- /dev/null
+++ b/NDTensors/src/lib/TypeParameterAccessors/src/ndims.jl
@@ -0,0 +1,6 @@
+struct NDims{ndims} end
+Base.ndims(::NDims{ndims}) where {ndims} = ndims
+
+NDims(ndims::Integer) = NDims{ndims}()
+NDims(arraytype::Type{<:AbstractArray}) = NDims(ndims(arraytype))
+NDims(array::AbstractArray) = NDims(typeof(array))
diff --git a/NDTensors/src/lib/TypeParameterAccessors/test/test_similartype.jl b/NDTensors/src/lib/TypeParameterAccessors/test/test_similartype.jl
index 703f9ba1e1..0813fc917b 100644
--- a/NDTensors/src/lib/TypeParameterAccessors/test/test_similartype.jl
+++ b/NDTensors/src/lib/TypeParameterAccessors/test/test_similartype.jl
@@ -1,15 +1,26 @@
 @eval module $(gensym())
 using Test: @test, @test_broken, @testset
-using LinearAlgebra: Adjoint
-using NDTensors.TypeParameterAccessors: similartype
+using LinearAlgebra: Adjoint, Diagonal
+using NDTensors.TypeParameterAccessors: NDims, similartype
 @testset "TypeParameterAccessors similartype" begin
   @test similartype(Array, Float64, (2, 2)) == Matrix{Float64}
-  # TODO: Is this a good definition? Probably it should be left unspecified.
-  @test similartype(Array) == Array{Any}
+  @test similartype(Array) == Array
   @test similartype(Array, Float64) == Array{Float64}
   @test similartype(Array, (2, 2)) == Matrix
+  @test similartype(Array, NDims(2)) == Matrix
+  @test similartype(Array, Float64, (2, 2)) == Matrix{Float64}
+  @test similartype(Array, Float64, NDims(2)) == Matrix{Float64}
   @test similartype(Adjoint{Float32,Matrix{Float32}}, Float64, (2, 2, 2)) ==
     Array{Float64,3}
+  @test similartype(Adjoint{Float32,Matrix{Float32}}, Float64, NDims(3)) == Array{Float64,3}
   @test similartype(Adjoint{Float32,Matrix{Float32}}, Float64) == Matrix{Float64}
+  @test similartype(Diagonal{Float32,Vector{Float32}}) == Matrix{Float32}
+  @test similartype(Diagonal{Float32,Vector{Float32}}, Float64) == Matrix{Float64}
+  @test similartype(Diagonal{Float32,Vector{Float32}}, (2, 2, 2)) == Array{Float32,3}
+  @test similartype(Diagonal{Float32,Vector{Float32}}, NDims(3)) == Array{Float32,3}
+  @test similartype(Diagonal{Float32,Vector{Float32}}, Float64, (2, 2, 2)) ==
+    Array{Float64,3}
+  @test similartype(Diagonal{Float32,Vector{Float32}}, Float64, NDims(3)) ==
+    Array{Float64,3}
 end
 end
diff --git a/NDTensors/src/lib/TypeParameterAccessors/test/test_wrappers.jl b/NDTensors/src/lib/TypeParameterAccessors/test/test_wrappers.jl
index d253f92c77..ed8e223922 100644
--- a/NDTensors/src/lib/TypeParameterAccessors/test/test_wrappers.jl
+++ b/NDTensors/src/lib/TypeParameterAccessors/test/test_wrappers.jl
@@ -11,6 +11,7 @@ using LinearAlgebra:
   UnitUpperTriangular,
   UpperTriangular
 using NDTensors.TypeParameterAccessors:
+  NDims,
   TypeParameter,
   is_wrapped_array,
   parenttype,
@@ -33,6 +34,7 @@ include("utils/test_inferred.jl")
     @test_inferred set_eltype(array, Float32) ≈ array
     @test_inferred set_eltype(Array{<:Any,2}, Float64) == Matrix{Float64}
     @test_inferred set_ndims(Array{Float64}, 2) == Matrix{Float64} wrapped = true
+    @test_inferred set_ndims(Array{Float64}, NDims(2)) == Matrix{Float64} wrapped = true
     @test_inferred set_ndims(Array{Float64}, TypeParameter(2)) == Matrix{Float64}
     @test_inferred unwrap_array_type(array_type) == array_type
   end