This paper proposes a new duty-based Smith Chart as part of an improved method of selecting the geometric topology of compressors (axial, mixed or radial) in the earliest stage of design. The method has a number of advantages over previous methods: it is based on the non-dimensional flow and the non-dimensional work, which aligns with the aerodynamic function of the compressor and is therefore more intuitive than specific speed and specific diameter. It is based on a large number of consistently designed compressor rotors which have been computationally predicted using RANS CFD. Most importantly, it provides the designer not only with a choice of topology but also with the complete meridional geometry of the compressor, its blade design and the number of blades. This fidelity of geometry at the very early stage of design allows the designer to undertake a true systems design optimization (noise, manufacturing, packaging constraints and cost). This has the major advantage of significantly reducing early stage design times and costs and allows the designer to explore completely new products more quickly.