[en] We have determined the structure of micelles formed in water by several classes of ionic surfactants under a variety of experimental conditions using small-angle neutron scattering (SANS) techniques. Contrast between the micelles and the solvent was achieved through either selective deuteration or fluorination of the surfactant, or through the use of D₂O. Interpretation of SANS data was facilitated by the use of Hayter, Penfold, and Hansen's rescaled Mean Spherical Approximation theory to calculate the scattering due to interparticle interactions. We have devised a number of micelle models, both spherical and ellipsoidal, to account for the scattering due to single micelles. It was found that changing the solvent from H₂O to D₂O results in the formation of larger micelles due to changes in the solvent-surfactant hydrocarbon interactions. This solvent isotope effect increased as the length of the alkyl chain increased. The fractional micellar charge did not change with respect to isotopic composition of solvent. We found that alkyltrimethylammonium bromide surfactants form drier micelles than do the sodium alkyl sulfate surfactants of equal chain length. Also, all micelles studied were found to be dry near the critical micelle concentration (cmc) and to become increasingly wetter as the concentration increased. The increase in aggregation number with respect to the square root of surfactant concentration was found to be linear for all systems studied. 80 figs