Aqueous solutions of fully ionized tetradecyldimethylamine oxide (TDAO) with addition of 0.1 M NaCl were investigated by small-angle neutron scattering (SANS) and static light scattering (SLS). The analysis of the data showed that the surfactant under these conditions forms short stiff cylindrical micelles. The surfactant concentration ranges from 2 times the critical micelle concentration to well above the overlap concentration of the cylindrical micelles. A self-consistent approach was used for analyzing the SANS and SLS data simultaneously. The forward scattering was determined from the scattering at low scattering vectors, and from this, the apparent molar mass of the micelles was derived. It was fitted by a model with a power-law growth law combined with a term which describes intermicellar interaction effects. The length of the micelles was derived from the growth law using the mass per unit length as determined from the scattering data at high scattering vectors. Finally, the data in the full range of measured scattering vectors were fitted for all concentrations by a model based on the polymer reference interaction site model with a simple ansatz for the direct correlation function. The variations of the parameters of the micelles as obtained in the analysis were compared to the parameters for solutions of half-ionized TDAO for which semiflexible micelles are formed.