The main driver for small scale turbomachinery in domestic heat pumps is the potential for reaching higher efficiencies than volumetric compressors currently used and the potential for making the compressor oil-free, bearing a considerable advantage in the design of advanced multi-stage heat pump cycles. An appropriate turbocompressor for driving domestic heat pumps with a high temperature lift requires the ability to operate on a wide range of pressure ratios and mass flows, confronting the designer with the necessity of a compromise between range and efficiency. The present publication shows a possible way to deal with that difficulty, by coupling an appropriate modeling tool to a multi-objective optimizer. The optimizer manages to fit the compressor design into the possible specifications field while keeping the high efficiency on a wide operational range. The 1D-tool used for the compressor stage modeling has been validated by experimentally testing an initial impeller design. The excellent experimental results, the agreement with the model and the linking of the model to a multi-objective optimizer will allow to design radial compressor stages managing to fit the wide operational range of domestic heat pumps while keeping the high efficiency level.