We present experimental data showing that the surface tension, a, of anionic surfactant (sodium dodecyl dioxyethylene sulfate : SDP-2S) solutions undergoes a substantial change in the vicinity of the transition from sphere to cylinder in the micelle shape. The formation of cylindrical (rodlike) micelles at relatively low surfactant concentrations (between 2 and 8 mM) is promoted by the presence of Al3+ ions in the solution. In the experiments we fixed the ionic strength of the added electrolyte but varied the molar fractions of NaCl and AlCl3. We established that the observed variation of sigma in a vicinity of the sphere-to-rod transition can be attributed to two competitive effects : (i) competition between Na+ and Al3+ counterions for the adsorption in the subsurface Stern layer and (ii) competition between the solution surface and the surfaces of the micelles to adsorb the Al3+ counterions. The concentration of free Al3+ ions in the solution is substantially reduced due to binding of Al3+ to the micelles. The latter effect is studied experimentally by means of ultrafiltration experiments. We develop a theoretical model that allows us to calculate the true bulk (background) concentrations of Na+ and Al3+ ions, and the variation of sigma in the vicinity of the sphere-to-rod transition. Good agreement between theory and experiment is achieved. The results show that the transition from sphere to cylinder in the micelle shape can be detected from the plot of the surface tension vs the surfactant-to-Al3+ ratio. The paper also contains experimental data for the dependence of the CMC and surface tension of SDP-2S solutions on the ionic strength, which may represent independent interest.