A molecular-thermodynamic theory of micellization of ionic surfactants, developed in paper 1 of this series, is applied here to specific ionic surfactant-electrolyte systems in order to test its ability to quantitatively predict various micellar solution properties, including the effect of the counterion hydrated size, valence, and lipophilicity. With this goal in mind, the theory is utilized to model surfactant solutions containing (i) monovalent counterions (specifically, the alkali metal dodecyl sulfate series, MDS), (ii) multivalent counterions (specifically, the sodium dodecyl dioxyethylene sulfate surfactant, SDE2S, with added AlCl3 + NaCl and CaCl2 + NaCl), and (iii) organic counterions (specifically, the alkyl trimethylammonium salicylate series, C(n)TASal). The predicted micellar solution properties include (i) the optimal degree of binding of each counterion species onto the charged micelle surface, (ii) the surfactant critical micelle concentration, and (iii) the optimal micelle shape and average micelle aggregation numbers. In the MDS surfactant series, a decrease in the hydrated size of the alkali metal counterion leads to an increase in the degree of counterion binding and to an increase in the average sizes of the micelles formed. In the SDE2S-AlCl3-NaCl and the SDE2S-CaCl2-NaCl surfactant systems, the degrees of binding of the multivalent counterion (Al3+ or Ca2+) and of the monovalent counterion (Na+) vary with the individual concentrations of the two added electrolytes, even when the overall solution ionic strength is kept constant. Moreover, at fixed ionic strength, as the proportion of the multivalent-ion-carrying electrolyte is increased, the degree of binding of the multivalent counterion increases, and the resulting reduction in the micelle surface charge leads to a shape transition from spherical to cylindrical micelles. In the C(n)TASal surfactant system, the hydrophobicity of the salicylate counterion promotes a higher degree of counterion binding onto the micelle surface, as compared to that of its chloride analogue, C(n)TAC, and leads to the aggregation of the C(n)TASal surfactants into cylindrical micelles as compared to the aggregation of the C(n)TAC surfactants into spherical micelles. In addition to reproducing the experimentally observed qualitative trends, our theoretically predicted micellar solution properties are found to be in good quantitative agreement with the available experimental results.