SDS wormlike micelles in water with NaBr are studied using small-angle neutron scattering. SDS concentrations ranging from 0.08 to 8.6 % vol in NaBr aqueous solutions at salinities from 0.6 to 1.0 M are covered. The scattering data are analyzed using a novel approach based on polymer theory and the results of Monte Carlo simulations. The method makes it possible to give a full interpretation of the scattering data, even for the entangled micellar solutions occurring at high concentrations and high salinities. Analysis of the scattering data at zero scattering angle demonstrates that the length of the micelles increases according to a power law as a function of concentration in the studied interval. The analysis furthermore shows that the length of the micelles increases exponentially with increasing salinity. The scattering data in the full range of scattering angles are analyzed using a model for polydisperse wormlike micelles where excluded volume effects are taken into account via an expression based on the polymer reference interaction site model (PRISM). This part of the analysis show that the micelles become more flexible as the salinity increases, which is due to an increased screening of the ionic micelles.