diff --git a/src/Batches/batch.jl b/src/Batches/batch.jl
index 10958516..4f0077d1 100644
--- a/src/Batches/batch.jl
+++ b/src/Batches/batch.jl
@@ -1,9 +1,11 @@
 # Batches
 
-struct Batch{T,S} <: BatchLike{T,S}
+struct Batch{T,S} <: Batchable{T,S}
   data::Storage{T,S}
 end
 
+storage(b::Batch) = b.data
+
 Batch(xs) = Batch(Storage(xs))
 
 convertel(T::Type, xs::Batch) =
@@ -18,8 +20,10 @@ tobatch(xs) = tobatch(batchone(xs))
 
 # Sequences
 
-struct Seq{T,S} <: BatchLike{T,S}
+struct Seq{T,S} <: Batchable{T,S}
   data::Storage{T,S}
 end
 
+storage(s::Seq) = s.data
+
 Seq(xs) = Seq(Storage(xs))
diff --git a/src/Batches/catmat.jl b/src/Batches/catmat.jl
index 43651e84..e91e9b75 100644
--- a/src/Batches/catmat.jl
+++ b/src/Batches/catmat.jl
@@ -1,42 +1,10 @@
 import Base: eltype, size, getindex, setindex!, convert, typename
 
-rawbatch(xs) = xs
-
-# Generic methods
-
-abstract type BatchLike{T,S} <: AbstractVector{T}
-end
-
-eltype{T}(::BatchLike{T}) = T
-
-rawbatch(xs::BatchLike) = rawbatch(xs.data)
-
-size(b::BatchLike) = (size(rawbatch(b), 1),)
-
-getindex(b::BatchLike, i)::eltype(b) = slicedim(rawbatch(b), 1, i)
-
-setindex!(b::BatchLike, v, i::Integer) = rawbatch(b)[i, :] = v
-
-function setindex!(b::BatchLike, xs, ::Colon)
-  for (i, x) in enumerate(xs)
-    b[i] = x
-  end
-end
-
-typerender(B::Type) = B
-typerender(B::Type{<:BatchLike}) =
-  Row(Juno.typ("$(typename(B).name)"), text"{", typerender(eltype(B)), text"}")
-
-@render Juno.Inline b::BatchLike begin
-  Tree(Row(typerender(typeof(b)),
-           Juno.fade("[$(length(b))]")),
-       Juno.trim(collect(b)))
-end
-
 # Concrete storage
 
-struct Storage{T,S} <: BatchLike{T,S}
+struct Storage{T,S}
   data::S
+  Storage{T,S}(data::S) where {T,S} = new{T,S}(data)
 end
 
 allequal(xs) = all(x -> x == first(xs), xs)
@@ -50,28 +18,79 @@ function Storage{T,S}(xs, storage::S) where {T, S}
   return Storage{T,S}(storage)
 end
 
-function Storage{T}(xs) where T
+function Storage{T,S}(xs) where {T,S}
   xs′ = map(rawbatch, xs)
-  storage = similar(first(xs′), (length(xs′), size(first(xs′))...))
+  storage = S(length(xs′), size(first(xs′))...)
   Storage{T,typeof(storage)}(xs′, storage)
 end
 
+Storage{T}(xs) where T = Storage{T,diminc(typeof(rawbatch(first(xs))))}(xs)
+
 Storage(xs) = Storage{eltype(xs)}(xs)
 
-convert{T,S}(B::Type{<:BatchLike{T,S}}, data::S) = B(data)
+convert{T,S}(::Type{Storage{T,S}}, data::S) = Storage{T,S}(data)
+
+convert{T}(::Type{Storage{T}}, data::AbstractArray) = convert(Storage{T,typeof(data)}, data)
+
+# Storage utility methods
+
+rawbatch(xs) = xs
+rawbatch(xs::Storage) = xs.data
+
+eltype{T}(::Storage{T}) = T
+
+size(b::Storage) = (size(b.data, 1),)
+
+getindex(b::Storage, i)::eltype(b) = slicedim(b.data, 1, i)
+
+setindex!(b::Storage, v, i::Integer) = b.data[i, :] = v
+
+function setindex!(b::Storage, xs, ::Colon)
+  for (i, x) in enumerate(xs)
+    b[i] = x
+  end
+end
+
+# Generic methods
+
+abstract type Batchable{T,S} <: AbstractVector{T}
+end
+
+rawbatch(xs::Batchable) = rawbatch(storage(xs))
+size(xs::Batchable) = size(storage(xs))
+getindex(xs::Batchable, i) = getindex(storage(xs), i)
+
+typerender(B::Type) = B
+typerender(B::Type{<:Batchable}) =
+  Row(Juno.typ("$(typename(B).name)"), text"{", typerender(eltype(B)), text"}")
+
+@render Juno.Inline b::Batchable begin
+  Tree(Row(typerender(typeof(b)),
+           Juno.fade("[$(length(b))]")),
+       Juno.trim(collect(b)))
+end
 
 # Horrible type hacks follow this point
 
 deparam(T::Type) = typename(T).wrapper
 
-dimless(T::Type{<:AbstractArray}) = ndims(T) == 1 ? eltype(T) : deparam(T){eltype(T),ndims(T)-1}
+diminc(T::Type) = Vector{T}
+diminc(T::Type{<:AbstractArray}) = deparam(T){eltype(T),ndims(T)+1}
 
-btype(B::Type{<:BatchLike}, S::Type{<:AbstractArray}) = B{dimless(S),S}
-btype(B::Type{<:BatchLike{T}} where T, S::Type{<:AbstractArray}) = B{S}
-btype(B::Type{<:BatchLike{<:BatchLike}}, S::Type{<:AbstractArray}) =
-  deparam(B){btype(eltype(B), dimless(S)),S}
+dimdec{T}(::Type{<:AbstractArray{T,1}}) = T
+dimdec(T::Type{<:AbstractArray}) = deparam(T){eltype(T),ndims(T)-1}
 
-convert{T<:BatchLike}(::Type{T}, xs::AbstractArray) =
-  convert(btype(T, typeof(xs)), xs)
+btype(B::Type, S::Type{<:AbstractArray}) = B
+btype(B::Type{<:Batchable}, S::Type{<:AbstractArray}) = B{dimdec(S),S}
+btype(B::Type{<:Batchable{T}} where T, S::Type{<:AbstractArray}) = B{S}
+btype(B::Type{<:Batchable{<:Batchable}}, S::Type{<:AbstractArray}) =
+  deparam(B){btype(eltype(B), dimdec(S)),S}
 
-convert{T<:BatchLike}(::Type{T}, x::T) = x
+convert{T<:Batchable}(::Type{Storage{T}}, data::AbstractArray) =
+  Storage{btype(T,dimdec(typeof(data))),typeof(data)}(data)
+
+convert{T,S<:AbstractArray}(B::Type{<:Batchable{T,S}}, data::S) = B(convert(Storage{T,S}, data))
+
+convert{B<:Batchable}(::Type{B}, data::AbstractArray) = convert(btype(B,typeof(data)), data)
+
+convert{B<:Batchable}(::Type{B}, xs::B) = xs