Small-scale turbomachines in domestic heat pumps reach high efficiency and provide oil-free solutions, which improve heat-exchanger performance and offer major advantages in the design of advanced thermodynamic cycles. An appropriate turbocompressor for domestic air based heat pumps requires the ability to operate on a wide range of inlet pressure, pressure ratios, and mass flows, confronting the designer with the necessity to compromise between range and efficiency. Further, the design of small-scale direct driven turbomachines is a complex and interdisciplinary task. Textbook design procedures propose to split such systems into subcomponents and to design and optimize each element individually. This common procedure, however, tends to neglect the interactions between the different components leading to suboptimal solutions. The author proposes an approach based on the integrated philosophy for designing and optimizing gas bearing supported, direct driven turbocompressors for applications with challenging requirements with regards to operation range and efficiency. Using experimentally validated reduced order models for the different components an integrated model of the compressor is implemented and the optimum system found via multi-objective optimization. It is shown that compared to standard design procedures, the integrated approach yields an increase of the seasonal compressor efficiency of more than 12 points. Further, a design optimization based sensitivity analysis allows to investigate the influence of design constraints determined prior to optimization such as impeller surface roughness, rotor material, and impeller force. A relaxation of these constrains yields additional room for improvement. Reduced impeller force improves efficiency due to a smaller thrust bearing mainly, whereas a lighter rotor material improves rotordynamic performance. A hydraulically smoother impeller surface improves the overall efficiency considerably by reducing aerodynamic losses. A combination of the relaxation of the three design constraints yields an additional improvement of six points compared to the original optimization process. The integrated design and optimization procedure implemented in the case of a complex design problem thus clearly shows its advantages compared to traditional design methods by allowing a truly exhaustive search for optimum solutions throughout the complete design space. It can be used for both design optimization and for design analysis.