This paper makes contributions in the area of predictive control and in particular examines to what extent different methods for parameterising the degrees of freedom within the input trajectories can improve aspects of feasibility and performance. A few earlier papers have suggested the potential for Laguerre polynomials to be effective within a predictive control design, but without giving explicit design guidelines. This paper extends that work by looking not only at systematic choices for the Laguerre parameters but also other choices of orthogonal functions. Systematic mechanisms are discussed to choose the best tuned alternative parameterisation dynamics. The efficacy of the proposed parameterisations within existing predictive control algorithms are demonstrated by examples.