A thermodynamic model is presented describing the equilibrium structure of micelles formed from ionic surfactants in diluted aqueous solutions at varying counterion concentrations. On a molecular level the model includes hydrophobic, steric, and electrostatic interactions. The conformational energy of the surfactant chain, direct adsorption of counterions to the micelle surface, and curvature effects are taken into account; By minimizing the Gibbs energy of the aggregates, the equilibrium structure is calculated for spherical, rod-shaped, and dumbbell-shaped micelles, the latter filling the gap between spheres and rods. To avoid edges, the dumbbells and the end caps of the rods are composed of a hemispherical and a catenoidal part. The Gibbs energy of the aggregates is used to determine the size distribution at given concentrations of surfactant and salt. From the size distributions the viscosity of the micellar solution is calculated and fitted to experimental viscosity data for hexadecylpyridinium chloride, bromide, iodide, and nitrate in diluted solutions with concentrations ranging up to 10 mM. Viscosity was measured at 50 degrees C with a capillary viscometer. The concentration of the anion was varied by the addition of the appropriate potassium salt. It is found that the tendency of rod formation increases in the order Cl-, Br-, NO3- I-. The viscosity calculated from the model is in good agreement with experimental data. According to the model, rods do not form unless the hydrocarbon/water interfacial tension increases with increasing curvature. Rod formation is favored by increasing counterion concentrations. Rods are always found to compete with dumbbells, while the contribution of spheres is negligible. The radius of the end caps of rod-shaped micelles is identical with the full chain length; that of the cylindrical part is smaller by about 0.3 nm. The head group area in the cylindrical part is only slightly smaller than that in the end cap and decreases with increasing counterion concentration. Since the Stokes radii are virtually the same for Cl-, Br-, I-, and NO3- counterion specificity cannot be attributed to Stokes radii. Instead it is modeled as a result of direct counterion adsorption. The model is also used to calculate the counterion association coefficients in dependence of counterion concentration.