In this paper we analyse tourism sustainability from a modelling point of view. The minimal model we propose is composed of three non-linear ordinary differential equations describing the dynamics of tourists, environment and services. Many of the parameters involved are concerned with the policy followed by agencies or local decision makers. A bifurcation analysis of the model is performed with respect to these parameters. Then, the notion of profitability and compatibility is introduced and used to interpret the bifurcation diagrams. The results are summarised in a few sustainability diagrams.