Sodium salicylate (NaSal) is added to aqueous solutions of cetyl trimethylammonium bromide (CTAB) to convert spherical micelles to wormlike micelles, thus producing an effective drag-reducing agent. A theoretical understanding of why NaSal is so effective at causing this transformation has not been developed at this time. Using a model that combines aspects of free energy models with simulations, we show change in ordering of the amphiphiles within the micelles of different curvatures. The way NaSal transforms the spherical micelles to wormlike micelles is by insertion of the salicylate ion into the surfactant shell, which reduces the preferred mean curvature of the surfactant shell and thus causes the transformation. This mechanism is different from that of a counterion shell formed in the presence of electrolytes. These models help us to understand the interactions between amphiphiles and additives in the micellar headgroups. The results of this model agree with some experimentally observed trends and help to account for others. Comparisons of our models with predictions based only on free energy models highlight the significance of accounting for intramicellar ordering in calculating micelle free energies. In general, such a model can predict the effect of the inclusion of other organic additives into micellar structures.