The solid-state potentiostatic technique is a convenient and versatile tool for studying oxygen transport in electronically conducting perovskites. Furthermore, a systematic analysis of the relaxation data helps elucidate the mechanistic nature of the prevalent oxygen rate process. As a case in point, we describe potential step measurements on 90% dense samples of SrCo1-xFexO3-delta, focusing per se on the assumptions underlying the technique and the interpretation of results. Careful analysis of the current-relaxation data pointed to the presence of high-diffusivity paths in the samples. It also indicated that the overall transport rate is controlled by an oxygen exchange reaction at the grain boundaries. This complication prevented unambiguous assessment of the chemical diffusion coefficient in this material. In addition, the analysis showed that wide disagreements in the oxygen chemical diffusion coefficients reported in the literature for doped perovskites may be attributed to differences in the sample quality (e.g., density, grain size, and distribution) and the measurement technique employed.