An optimisation methodology in high-performance liquid chromatography (HPLC) is presented for the selection of two or more mobile phases having an optimal complementary resolution. The complementary mobile phases (CMPs) are selected in such a way that each one resolves optimally only some compounds in the mixture, while the remainder, resolved by the other mobile phase(s), can overlap among them. The methodology is based on the computation of a peak purity measurement for each solute, using an asymmetrical peak model for peak simulation. Two global resolution criteria (product of elementary resolutions and worst elementary resolution) and two methods for solving the problem (a systematic examination of all possible solute arrangements, and the use of genetic algorithms to expedite the calculation time) were used to find the optimal CMPs. The CMP optimisation methodology was applied to the resolution of a mixture of 10 diuretics and beta-blockers, which could not be resolved using a single mobile phase; virtual baseline resolution was achieved, however, with two CMPs.