With limited resources, time spent refining a design is time not spent in selecting its optimal configuration. A multi-fidelity optimization scheme is applied to the configuration and refinement of a generic core engine compression system. The best designs result from expending between half and three quarters of the total design effort on configuration selection. The performance of the refinement phase is a weak function of the preceding configuration phase when the latter is well into diminishing returns. By exploiting this behavior, the time taken to obtain equally good designs with the same analysis tools and computational resource may be halved.