This paper presents a systematic methodology for designing move blocking strategies to reduce the complexity of a model predictive controller for linear systems, with explicit optimisation of the blocking structure using mixed-integer programming. Given a move-blocked predictive controller with a terminal invariant set constraint for stability, combined with an input parameterisation to preserve recursive feasibility, two different optimisation problems are formulated for blocking structure selection. The first problem calculates the maximum achievable reduction in the number of input decision variables and prediction horizon length, subject to the controller's region of attraction containing a specified subset of the state space. Then, for a given fixed horizon length and block count determined by hardware capabilities, the second problem seeks to maximise the volume of an inner approximation to the region of attraction. Numerical examples show that the resulting blocking structures are able to optimally reduce controller complexity and improve region of attraction volume. (C) 2015 Elsevier Ltd. All rights reserved.