Casing treatments (CTs) have proven their potential to increase the working range of a compressor stage,
sometimes even with little or no decrease in efficiency. However, a positive impact on efficiency is only possible
if the additional CT-losses are compensated by a reduction of other losses, especially at rotor tip. This appears
to be increasingly difficult to achieve for highly efficient modern rotors. In order to analyse how CTs can
contribute to improve the overall compressor design, extensive optimization studies are performed, aiming
at increasing the stability and efficiency of a transonic compressor stage. Axial-slot CTs and the rotor are
optimized separately with a high number of geometric parameters. Selected Pareto-optimal geometries of
the two optimizations are combined to study various CTs on different rotors. It is shown that a significant
increase in stability can be achieved using axial-slot CTs, exceeding the values that can be reached optimizing
the rotor without CTs. However, no combination of optimized rotors and CTs is found that dominates the other
geometries in terms of efficiency. Hence, the question whether a CT can contribute to an improved compressor
design very much depends on the desired stage design. CTs provide a benefit if a maximum stability range is
necessary or if certain design choices lead to a demand for a stability enhancement, that otherwise cannot be
achieved. In order to gain a maximum efficiency, a design without CTs appears to be more promising in the
first place. Designs with comparably high losses in the rotor tip region, e.g. due to large tip clearances, might
also benefit of CTs in terms of efficiency