Small-angle neutron scattering measurements on sodium dodecyl sulfate aqueous solutions have been performed in the presence of n-alcohols, from methanol to octanol, at different alcohol concentrations. By modeling the experimental intensities, it was possible to obtain structural information and to derive simultaneously the distribution of the alcohols between the aqueous and the micellar phases. It was found that short chain alcohols tend to remain in the aqueous phase and, by altering the solvent properties, induce a decrease in the aggregation number of sodium dodecyl sulfate micelles. On the other hand, alcohols with longer hydrocarbon chains were found to be present in both phases though favoring the micellar phase the longer the alkyl chain and the larger the concentration; this could be rationalized by assuming that the insertion of alcohol molecules in the micelle produced weaker repulsive interactions between the charged head groups of the surfactant molecules. For long chain alcohols, appreciably localized in the micellar phase, screening of the interaction among head groups leads to bigger micelles than those observed in the absence of alcohol : in these cases the alcohol/surfactant molar ratio reaches the value of 0.86, and hence the aggregates can be considered as mixed micelles. Sodium dodecyl sulfate micelles, at the examined concentration, were found to deviate from spherical symmetry and, when added with heptanol or octanol, assumed an ellipsoidal shape growing preferentially along the rotation axis.