  We introduce the multi-width of a lattice polytope and use this to classify
and count all lattice tetrahedra with multi-width $(1,w_2,w_3)$. The approach
used in this classification can be extended into a computer algorithm to
classify lattice tetrahedra of any given multi-width. We use this to classify
tetrahedra with multi-width $(2,w_2,w_3)$ for small $w_2$ and $w_3$ and make
conjectures about the function counting lattice tetrahedra of any multi-width.
