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Electrification of buildings through deployment of heat pumps requires innovative design and control strategies to reduce their energy demands on the grid. Instead of the sequential approach of optimizing the design specifications and control strategies, this paper considers the benefits of the combined and simultaneous optimization of design capacities and control settings for heat pumps when specified for US residential buildings. A Genetic Algorithm optimizer is used to simultaneously adjust the main and supplementary coil capacities for the heat pump as well as the indoor temperature setpoints to minimize annual heating and cooling energy needs as well as occupant thermal discomfort levels. In comparison to design and control baselines, it is found that simultaneous optimization can achieve 21% and 7% reductions in heating and cooling annual energy consumption for the cases of variable speed and single speed heat pumps. Moreover, the analysis results indicate that these reductions are nearly double the savings obtained when design only and control only based optimizations are considered. The presented combined design and control optimization approach could potentially provide an effective paradigm shift in specifying heat pump systems for residential buildings.