This paper gives new insight and design proposals for Predictive Functional Control (PFC) algorithms. Common practice and indeed a requirement of PFC is to select a coincidence horizon greater than one for high-order systems and for the link between the design parameters and the desired dynamic to be weak. Here the proposal is to use parallel first-order models to form an independent prediction model and show that with these it is possible both to use a coincidence horizon of one and moreover to obtain precisely the desired closed-loop dynamics. It is shown through analysis that the use of a coincidence horizon of one greatly simplifies coding, tuning, constraint handling and implementation. The paper derives the key results for high-order and non-minimum phase processes and also demonstrates the flexibility and potential industrial utility of the proposal. •Extending the ease and efficacy of tuning for PFC to higher order processes.•Computationally efficient and easy to code predictive control algorithms.•Analysis and insights into the PFC approach to control design.