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.