Disturbances in the presence of constraints can drive predictive control into infeasibility and instability. This problem has attracted little research effort, despite its significant practical importance. Earlier work has given stability conditions, but these are restricted to systems with at most one unstable pole, and do not lead to suitable algorithms because they apply to infinite horizons only. Here we modify the constraint limits and derive an algorithm with guaranteed stability and asymptotic tracking. Available degrees of freedom are given up in order to optimize performance; the results of the paper are illustrated by means of numerical examples.