  We present a practical algorithm to compute models of rational functions with
minimal resultant under conjugation by fractional linear transformations. We
also report on a search for rational functions of degrees 2 and 3 with rational
coefficients that have many integers in a single orbit. We find several minimal
quadratic rational functions with 8 integers in an orbit and several minimal
cubic rational functions with 10 integers in an orbit. We also make some
elementary observations on possibilities of an analogue of Szpiro's conjecture
in a dynamical setting and on the structure of the set of minimal models for a
given rational function.
