Predictive control strategies allow for the systematic handling of constraint, performance and stability. However, the associated algorithms can be computational burdensome and/or difficult to unravel. The aim of this paper is to discuss and compare algorithms based on invariant sets which meet the additional requirement for computational simplicity. There may of course be a concomitant loss of optimality, but as illustrated, this can be minimal and often is a small price to pay when one considers the significant improvements in efficiency.