Wide-angle neutron scattering experiments combined with Empirical Potential Structural Refinement modelling have been used to study the detailed structure of decyltrimethylammonium bromide micelles in the presence of acid solutions of HCl or HBr. These experiments demonstrate considerable variation in micelle structure and water structuring between micelles in the two acid solutions and in comparison with the same micelles in pure water. In the presence of the acids, the micelles are smaller, however in the presence of HCl the micelles are more loosely structured and disordered while in the presence of HBr the micelles are more compact and closer to spherical. Bromide ions bind strongly to the micelle surface in the HBr solution, while in HCl solutions, ion binding to the micelle is similar to that found in pure water. The hydration numbers of the anions and extent of counterion binding follow the predictions of the Hofmeister series for these species.