Generalized predictive control, with and without endpoint constraints, was developed in the context of discrete-time systems and recent work developed an interesting framework for an extension to continuous-time systems. The present paper gives further consideration to the implied prediction class and proposes improvements with respect to optimality and the guarantee of stability. In addition by proposing a simple extension of the prediction class so as to include the l(2) optimal solution, in this paper we derive further improvements which can also be applied to the case when the system inputs are subject to physical limits.