Computer simulation software for solvent strength optimization and statistical mixture design based on the solvent | selectivity triangle were useful tools employed for the development of a reversed-phase HPLC method to separate duloxetine, a new anti-depressant compound, and structurally-related impurities. Solvent strength optimization was used to show that adequate separation for all impurities could not be obtained with a single organic modifier and to aid in choosing appropriate boundary conditions for a mixture design study. The mixture design was used to obtain resolution maps for organic modifier mixtures consisting of acetonitrile, methanol, and tetrahydrofuran. Overlapping resolution maps for the peak pairs of interest revealed the solvent composition that would provide the maximum resolution. Finally, solvent strength was optimized at the best solvent composition and information about method robustness obtained.