Input- and output-split hybrids, which use a single planetary gear (PG), have a good fuel economy, but a relatively low acceleration performance. In order to improve their acceleration performance, speed reduction gears (SRG) have been employed in various commercialized split hybrids. However, the full potential of using SRGs has not yet been investigated. In fact, adding one SRG to input- or output-split hybrids can improve not only their acceleration performance, but also their fuel economy. Nevertheless, the design space of input- and output-split configurations using one SRG is huge; 864 configurations are using two PGs connected through one interconnection and having one node grounded to a fixed platform. Thus, in order to solve this high computational load problem, an efficient comprehensive design methodology is highly required. This paper proposes a systematic compound lever based design methodology used to analyze the entire design space of input- and output-split hybrids using one SRG and to find outstanding configurations in terms of both fuel economy and acceleration performance. In this study, the compound lever was used as a design tool rather than for modelling to guarantee the efficient analysis of the entire design space through omitting redundant configurations having the same performance. Dynamic programming was used to assess the performance metrics of the entire designs and the fuel economy and acceleration performance trends were observed to select optimal configurations. Then, as the compound lever lacks physical information required for the realization of novel powertrains, optimal compound levers selected were converted into feasible powertrain configurations. Throughout this study, the impact of using an additional PG as SRG was studied as the obtained results were compared to those of single PG configurations. Besides, various outstanding configurations were obtained, which have a better performance than the commercialized ones such as Toyota Prius third generation.