The bismuthinite - aikinite (Bi₂S₃ - CuPbBiS₃) series of ordered derivatives (superstructures) is based on the incremental Bi + vacancy Pb + Cu substitution. Selected structures of this series, gladite, salzburgite, paarite and krupkaite, were refined as commensurately modulated structures using the superspace approach. The superspace group Pmcn(0ß0)00s was used for all these structures, ß assuming the value of 1/3, 1/4, 1/5, and 2 in the above order. Two independent large-cation positions, one Cu position (in oversubstituted members, two) and three S positions were refined for the sequence of one or three to five subcells forming the above structures using the summation of sinusoidal functions for positional and displacement parameters. In this paper, we describe, in terms intended for non-specialists, our choice of the superspace group, its application to individual superstructures, the details of the structure refinement, and the structural interpretation of the results.