diff --git a/Project.toml b/Project.toml
index 9127905..cd5c2ce 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "TypeParameterAccessors"
 uuid = "7e5a90cf-f82e-492e-a09b-e3e26432c138"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.3.1"
+version = "0.3.2"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
diff --git a/src/base/abstractarray.jl b/src/base/abstractarray.jl
index 0316e3c..a5a2f91 100644
--- a/src/base/abstractarray.jl
+++ b/src/base/abstractarray.jl
@@ -1,3 +1,10 @@
+struct Self end
+position(a, ::Self) = Position(0)
+position(::Type, ::Self) = Position(0)
+function set_type_parameters(type::Type, ::Self, param)
+  return error("Can't set the parent type of an unwrapped array type.")
+end
+
 position(::Type{AbstractArray}, ::typeof(eltype)) = Position(1)
 position(::Type{AbstractArray}, ::typeof(ndims)) = Position(2)
 default_type_parameters(::Type{AbstractArray}) = (Float64, 1)
@@ -9,14 +16,6 @@ default_type_parameters(::Type{<:Array}) = (Float64, 1)
 position(::Type{<:BitArray}, ::typeof(ndims)) = Position(1)
 default_type_parameters(::Type{<:BitArray}) = (1,)
 
-struct Self end
-position(a, ::Self) = Position(0)
-position(::Type{T}, ::Self) where {T} = Position(0)
-
-function set_type_parameters(type::Type, ::Self, param)
-  return error("Can't set the parent type of an unwrapped array type.")
-end
-
 function set_eltype(array::AbstractArray, param)
   return convert(set_eltype(typeof(array), param), array)
 end
diff --git a/src/type_parameters.jl b/src/type_parameters.jl
index 31e6ca0..b0bc681 100644
--- a/src/type_parameters.jl
+++ b/src/type_parameters.jl
@@ -27,10 +27,62 @@ function position end
 position(object, name) = position(typeof(object), name)
 position(::Type, pos::Int) = Position(pos)
 position(::Type, pos::Position) = pos
+
 function position(type::Type, name)
-  base_type = unspecify_type_parameters(type)
-  base_type === type && error("`position` not defined for $type and $name.")
-  return position(base_type, name)
+  type′ = unspecify_type_parameters(type)
+  if type === type′
+    # Fallback definition that determines the
+    # position automatically from the supertype of
+    # the type.
+    return position_from_supertype(type′, name)
+  end
+  return position(type′, name)
+end
+
+# Automatically determine the position of a type parameter of a type given
+# a supertype and the name of the parameter.
+function position_from_supertype(type::Type, name)
+  type′ = unspecify_type_parameters(type)
+  supertype_pos = position(supertype(type′), name)
+  return position_from_supertype_position(type′, supertype_pos)
+end
+
+# Automatically determine the position of a type parameter of a type given
+# the supertype and the position of the corresponding parameter in the supertype.
+@generated function position_from_supertype_position(
+  ::Type{T}, supertype_pos::Position
+) where {T}
+  T′ = unspecify_type_parameters(T)
+  # The type parameters of the type as TypeVars.
+  # TODO: Ideally we would use `get_type_parameters`
+  # but that sometimes loses TypeVar names:
+  # https://github.com/ITensor/TypeParameterAccessors.jl/issues/30
+  type_params = Base.unwrap_unionall(T′).parameters
+  # The type parameters of the immediate supertype as TypeVars.
+  # This has TypeVars with names that correspond to the names of
+  # the TypeVars of the type parameters of `T`, for example:
+  # ```julia
+  # julia> struct MyArray{B,A} <: AbstractArray{A,B} end
+  #
+  # julia> Base.unwrap_unionall(MyArray).parameters
+  # svec(B, A)
+  #
+  # julia> Base.unwrap_unionall(supertype(MyArray)).parameters
+  # svec(A, B)
+  # ```
+  supertype_params = Base.unwrap_unionall(supertype(T)).parameters
+  supertype_param = supertype_params[Int(supertype_pos)]
+  pos = findfirst(param -> (param.name == supertype_param.name), type_params)
+  if isnothing(pos)
+    return error("Position not found.")
+  end
+  return :(@inline; $(Position(pos)))
+end
+
+# Automatically determine the position of a type parameter of a type given
+# a supertype and the name of the parameter.
+function position_from_supertype(type::Type, supertype_target::Type, name)
+  return position_from_supertype(type, supertype_target, position(supertype_target, name))
 end
 
 function positions(::Type{T}, pos::Tuple) where {T}
diff --git a/test/test_basics.jl b/test/test_basics.jl
index 29e5b7f..a668232 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -2,7 +2,12 @@ using JLArrays: JLArray, JLMatrix, JLVector
 using Test: @test, @test_throws, @test_broken, @testset
 using TestExtras: @constinferred
 using TypeParameterAccessors:
-  set_type_parameters, specify_type_parameters, type_parameters, unspecify_type_parameters
+  TypeParameterAccessors,
+  Position,
+  set_type_parameters,
+  specify_type_parameters,
+  type_parameters,
+  unspecify_type_parameters
 
 const anyarrayts = (
   (arrayt=Array, matrixt=Matrix, vectort=Vector),
@@ -78,3 +83,30 @@ const anyarrayts = (
       (3, Float32)
   end
 end
+
+@testset "Automatic fallback for position" begin
+  struct MyArray{B,A} <: AbstractArray{A,B} end
+  @test @constinferred(TypeParameterAccessors.position(MyArray, eltype)) == Position(2)
+  @test @constinferred(TypeParameterAccessors.position(MyArray{3,Float32}, eltype)) ==
+    Position(2)
+  @test @constinferred(TypeParameterAccessors.position(MyArray, ndims)) == Position(1)
+  @test @constinferred(TypeParameterAccessors.position(MyArray{3,Float32}, ndims)) ==
+    Position(1)
+
+  struct MyVector{X,Y,A<:Real} <: AbstractArray{A,1} end
+  @test @constinferred(TypeParameterAccessors.position(MyVector, eltype)) == Position(3)
+  @test @constinferred(
+    TypeParameterAccessors.position(MyVector{Int,(1, 2),Float32}, eltype)
+  ) == Position(3)
+  @test_throws ErrorException TypeParameterAccessors.position(MyVector, ndims)
+  @test_throws ErrorException TypeParameterAccessors.position(
+    MyVector{Int,(1, 2),Float32}, ndims
+  )
+
+  struct MyBoolArray{X,Y,Z,B} <: AbstractArray{Bool,B} end
+  @test_throws ErrorException TypeParameterAccessors.position(MyBoolArray, eltype)
+  @test_throws ErrorException TypeParameterAccessors.position(MyBoolArray{1,2,3,4}, eltype)
+  @test @constinferred(TypeParameterAccessors.position(MyBoolArray, ndims)) == Position(4)
+  @test @constinferred(TypeParameterAccessors.position(MyBoolArray{1,2,3,4}, ndims)) ==
+    Position(4)
+end