This paper considers the efficacy of disturbance models for ensuring offset-free control and the determination of the optimum feasible steady-state target within linear model predictive control (MPC). Previously proposed methods for steady-state target determination can address model error, disturbances, and output target changes when the desired steady state is feasible, but may fail to achieve a feasible target that is as close as possible to the desired steady-state target when the desired target is unreachable due to active constraints. Under certain conditions, the resulting 'feasible steady-state target' can converge to a point that is not as close as possible to the optimal feasible target. By considering the Karush-Kuhn-Tucker (KKT) conditions of optimality for the steady-state target optimizer, sufficient multi-variable conditions are established for which convergence to the optimal feasible target is guaranteed and, conversely, when convergence to a sub-optimal feasible target is expected. (C) 2010 Elsevier Ltd. All rights reserved.