On-chip capacity for storing temporal photon data in direct time-of-flight (dToF) lidar sensors is limited. This has prompted the development of various partial histogram approaches to reduce the amount of data stored on-chip. The aim of this paper is to inform sensor design by providing a taxonomy of these approaches, models for evaluating their impact on system laser power and identification of additional trade-offs which must be considered. All published on-chip partial histogram lidar approaches to-date are reviewed and two main categories are established: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zooming</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sliding.</i> A means of evaluating any specific configuration based on its histogram reduction ratio (HRR) is also established. To quantitatively evaluate partial histogram approaches, a model to determine the minimum number of required laser cycles is developed. Both zooming and sliding are compared to an ideal baseline using this model, in order to establish a laser power penalty benchmark for each approach. These are evaluated over a range of real-world design conditions for two contrasting designs: short-range indoor and long-range outdoor. In general, a sliding approach is found to be the most laser power-efficient for long-range outdoor applications, while a zooming approach becomes increasingly more effective under low ambient conditions. Power efficient <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cycle-scaled</i> variations on the conventional zooming and sliding approaches are introduced. These are shown to consistently reduce the laser power penalty across all tested design conditions. It is also shown that a cycle-scaled sliding histogram approach can be adopted to reduce the required on-chip histogram storage capacity by half, with almost no additional laser power penalty. Finally, a qualitative discussion of zooming and sliding compares additional key design considerations such as sensitivity to motion artefacts.