The expanded Hansen method is tested with two anti-inflammatory drugs, piroxicam (preferentially Lewis base) and niflumic acid (preferentially Lewis acid). The original dependent variable, ln α2/U, where α is the activity coefficient and U is related to the molar volume of the solute and the volume fraction of the solvent, was compared with the direct use of the logarithm of the mole fraction solubility ln X2 in the three- and four parameter models. The activity coefficient of the drugs was calculated from the heat and temperature of fusion before and after equilibration of each solid phase with the pure solvents used. The dependent variables ln X2 and ln α2/U provided similar partial solubility parameter values for piroxicam with the four parameter model. All the partial parameters of niflumic acid were significant statistically only with the variable ln X2. This indicates that ln X2 is the most suitable variable for the determination of partial solubility parameters. The dispersion solubility parameters are similar for both drugs, the largest differences being observed for the dipolar and hydrogen bonding parameters. The partial solubility parameters give insights into the interaction capability of the drugs and are consistent with their chemical structure. For niflumic acid, a better proton donor, δa>δb whereas for piroxicam, a preferentially Lewis base δb>δa. This result is particularly interesting as it demonstrates for the first time the validity of the method for a mainly proton-acceptor compound.