Power-split hybrid-electric vehicles (HEVs) employ two power paths between the internal combustion (IC) engine and the driven wheels routed through gearing and electric machines (EMs) composing an electrically variable transmission (EVT). The EVT allows IC engine control such that rotational speed can be independent of vehicle speed at all times. By breaking the rigid mechanical connection between the IC engine and the driven wheels, the EVT allows the IC engine to operate in the most efficient region of its characteristic brake specific fuel consumption (BSFC) map. If the most efficient IC engine operating point produces more power than is requested by the driver, the excess IC engine power can be stored in the energy storage system (ESS) and used later. Conversely, if the most efficient IC engine operating point does not meet the power request of the driver, the ESS delivers the difference to the wheels through the EMs. Therefore with an intelligent supervisory control strategy, power-split architectures can advantageously combine traditional series and parallel power paths.Previous work compared two different power-split HEV powertrains using a 2-term cost function and steady-state backward-looking simulation (BLS). BLS was used to find battery power management strategies resulting in minimized fuel consumption over a user-defined drive-cycle. The supervisory control strategy design approach amounts to an exhaustive search over all kinematically admissible engine and EM operating points, leading to a minimized instantaneous cost function. While the approach provides a valuable comparison of two architectures, non-ideal engine speed fluctuations result, preventing the control strategy from being effectively implemented. In the present work, two approaches are investigated for refining IC engine state transitions for use in an implemented control strategy: i) smoothing the 2-term cost function optimization results, and ii) introducing a 3-term cost function. These approaches are tested and verified in high-fidelity forward-looking simulations (FLSs). It is found that both refinement approaches effectively reduce engine speed transitions, and result in fuel economy (FE) estimates and component operation which compare well to BLS results. It is further found that the 3-term cost function finds more efficient operating points than the smoothed 2-term cost function approach. From the investigations carried out in this paper, a two-phase control strategy development process is suggested where control strategies are first explored using highly-efficient steady-state BLS models, and then further tested and refined in high-fidelity FLS models. Favorable comparison of BLS and FLS results justify the efficacy of the two-phased process, suggesting rapid and effective development of implementable power-split HEV supervisory control strategies.