Abstract
In the following essay we shall describe models for the theory MINPAR, the theory for finite binary trees, described in Jervell [2003]. In particular we shall investigate non-standard models simpler than the one presented by Roger, denotedM*. These include the models for both right and left oriented w-ladders and the zik-zak model. We believe that M* is the maximal nonstandard model for MINPAR, and that it is constructively inaccessible from any simpler model, not only those presented in the paper.