A combinatorial model for a property of continuous self-maps of a compact interval is a self-map \pi of a finite ordered set such that every continuous \pi-weakly monotone self-map of a compact interval has that property. We identify the minimal combinatorial models for the property ‘the set of periods is a given set’. Here the word minimal refers to the number of points in the domain of the model. We also identify the minimal permutation models and, in appropriate cases, the minimal combinatorial models for properties involving ‘horseshoes’.