A SANS study of 0.073 c micellar solutions of sodium alkyl sulfates with chain length from n(C) = 9 to 16 was carried out. Micelles were assumed to be ellipsoids which may grow only in the direction of their axis of symmetry. The structure factor was calculated in terms of the one-component macrofluid model by assuming DLVO potential. The contact radius and the strength of the interaction potential were handled as free fitting parameters; the electrostatic potential and the apparent micellar charge on the contact surface were derived from the latter, The assumptions imposed on the conformation of the micellar cores are sustained by the best-fit parameters of the form-factor. For n(C) = 9-13 the mean aggregation numbers are in good, or at least, in acceptable agreement with the predictions of a recent thermodynamic theory of micellization. The difference found between the mean core and contact radii suggests that an unknown repulsive interaction may be present which prevents the micelles from a-structurally possible-closer approach. Although the surface potential indicates that the outgoing conditions for deriving the DLVO potential are violated, the agreement of the electric charge derived partly from the DLVO potential, partly from the nonlinearized Gouy-Chapman model supports the practical applicability of the well-known DLVO potential formula to interpreting SAS results.