We use atomistic molecular dynamics simulations to probe the effects of added sodium chloride (NaCl) and sodium salicylate (NaSal) salts on the spherical-to-threadlike micelle shape transition in aqueous solutions of cetyltrimethylammonium chloride (CTAC) surfactants. Long threadlike micelles are found to be unstable and break into spherical micelles at low concentrations of NaCl, but remain stable for 20 ns above a threshold value of [NaCl] approximately 3.0 M, which is about 2.5 times larger than the experimental salt concentration at which the transition between spherical and rodlike micelles occurs. The chloride counterions associate weakly on the surface of the CTAC micelles with the degree of counterion dissociation decreasing slightly with increasing [NaCl] on spherical micelles, but dropping significantly on the threadlike micelles at high [NaCl]. This effect indicates that the electrolyte ions drive the micellar shape transition by screening the electrostatic repulsions between the micellar headgroups. The aromatic salicylate counterions, on the other hand, penetrate inside the micelle with their hydrophilic groups staying in the surfactant headgroup region and the hydrophobic groups partially embedded into the hydrophobic core of the micelle. The strong association of the salicylate ions with the surfactant headgroups leads to dense packing of the surfactant molecules, which effectively reduces the surface area per surfactant, and increases intramicellar ordering of the surfactant headgroups, favoring the formation of long threadlike micelles. Simulation predictions of the geometric and electrostatic properties of the spherical and threadlike micelles are in good agreement with experiments.