Terminal constraints guarantee the stability of predicted trajectories and form the basis of predictive control algorithms with guaranteed stability. Earlier work in the literature uses terminal constraints which define sufficient but not necessary conditions for tile stability of predicted trajectories. In this paper we deploy conditions which are both necessary and sufficient and hence release more degrees of freedom for optimizing performance and/or meeting constraints. Also an alternative means of computing the implied infinite horizon GPC cost, avoiding the need for solving a Lyapunov equation, is presented.