A practical interpolative technique for the preliminary design of a complex triplet lens using Cruickshank's analysis and Buchdahl's optical aberration coefficients is described. The technique, based on the mapping of the coefficients, is used to investigate the seventh-order solutions of a triplet lens with a view to systematically controlling the zonal spherical aberration. It is shown that monochromatic solutions of the Hektor type, generated from a particular region of the basic parameters, have third, fifth and seventh-order spherical coefficients of small value that alternate in sign.