This papers proposes new ways to enforce convergence to equilibria for Economic Model Predictive Control schemes. Economic Model Predictive Control is a control technique capable of optimizing an economic performance index while enforcing state and input constraints. For nonlinear systems and/or non-convex cost functionals, performance optimization may result in non converging behaviours. While this might be acceptable in some cases (i.e. operation of chemical reactors), it may be undesirable for other types of applications. In the present paper we discuss ways of enforcing convergence to equilibrium by trading it off with asymptotic performance. Indeed, while all trajectories converging to a given equilibrium yield the same asymptotic average cost, transient costs may differ and trade-offs are naturally highlighted between the latter and speed of convergence.