To interpret quantitatively experimental data for the growth of rodlike anionic surfactant micelles in the presence of Al3+ ions, we undertook experimental and theoretical investigations. We determined the micelle size, shape, and interactions by light scattering and examined the binding of Al3+ ions to the micelles by ultrafiltration. Independent static and dynamic light scattering measurements indicated that the effect of the micelle-micelle interactions in these solutions can be neglected. The major factor promoting the micelle growth turns out to be the binding of Al3+ ions to the micelle surfaces, which considerably affects the standard chemical potential of the aggregated surfactant molecules and can alter the micellization constant by orders of magnitude. The latter effect was described theoretically. The model of micelle growth, extended in this way, compared well with the experimental data. The model provides a quantitative description of the micelle size and charge as functions of the surfactant and electrolyte concentrations. It turns out that the rodlike micelles have a lower surface charge than the spherical ones, and this makes their growth energetically favorable. A practical application may follow from the markedly greater solubilization efficiency of the studied rodlike micelles compared to the spherical ones.