  We give upper bounds on the minimal degree of a model in $\mathbb{P}^2$ and
the minimal bidegree of a model in $\mathbb{P}^1 \times \mathbb{P}^1$ of the
curve defined by a given Laurent polynomial, in terms of the combinatorics of
the Newton polygon of the latter. We prove in various cases that this bound is
sharp as soon as the polynomial is sufficiently generic with respect to its
Newton polygon.
