Current self-tuning literature suggests that there are two principal strategies for controlling industrial processes using modern control theory: 'optimal' control where usually a quadratic cost is minimised over a finite or possibly infinite horizon, or the 'sub-optimal' approach of choosing the closed-loop pole positions. This paper demonstrates that in fact this arbitrary division is unnecessary and both approaches can be realised using a Generalised Predictive Control framework; it is shown that both LQ and Pole-placement control can be represented as predictive controllers. This property is then further explored to derive stability characteristics for the GPC approach. These results are verified by a series of examples and simulations concluding with a general set of guidelines for the use of different tuning 'knobs' of the GPC self-tuner.