Advanced cooling systems with high-temperature cooling (sensible only), night precooling, and highly efficient variable-speed compressors, fans, and pumps can benefit from on-line model predictive control to find and continually update optimal daily (or weekly) precooling sequences. As a part of the model predictive control, it is desirable to use optimized plant-specific control laws to match compressor, fan, and pump speeds to required capacity. A previous work presented a modular heat pump model that simulated steady-state performance over wide ranges of lift (external pressure ratios from <1 to 6) and capacity (10:1 turndown) that could be explored in the search for optimal solutions. This article describes the adaptive grid search technique used to map optimal heat pump performance as a function of the capacity and indoor and outdoor temperatures. The grid search finds optimal condenser and evaporator airflows and optimal subcooling at each operating point. The method is illustrated for a number of cases, including two-compressor systems and refrigerants R410A, R600 (propane), and R717 (ammonia). The non-linearity of optimal fan-speed control laws is demonstrated. The impact of zero subcooling with respect to optimal subcooling is assessed for the single compressor machines. The specific power at optimal fan speeds, as a function of capacity and indoor–outdoor temperature, is compared for R410A, propane, and ammonia-charged machines. Finally, the question of optimal sizing of optimally controlled variable-speed heat pumps is explored, and it is shown that modest oversizing is desirable. These findings suggest that the relative sizing of heat pump components—compressor, compressor motor, condenser, and evaporator—as well as the sizing of the heat pump itself relative to design load, may benefit from a thorough reassessment of current practice.