The structure of aggregates formed in aqueous mixtures of a single-chain anionic surfactant, sodium dodecyl sulfate (SDS), and a double-chain cationic surfactant, didodecyldimethylammonium bromide (DDAB), has been investigated at 38 degrees C using small-angle neutron scattering (SANS). Several overall surfactant concentrations [SDS] + [DDAB] between 0.1 and 5 wt % were measured at the two SDS-rich compositions [SDS]:[DDAB] = 90:10 and 95:5. Samples with a concentration above about [SDS] + [DDAB] = 1 wt % at [SDS]:[DDAB] = 95:5 contained only somewhat elongated tablet-shaped micelles (triaxial ellipsoids) with typical values of the half-axes a (related to the thickness) = 14 Angstrom, b (related to the width) = 23 Angstrom, and c (related to the length) = 27 Angstrom. When a sample at [SDS]:[DDAB] = 95:5 is diluted below about [SDS] + [DDAB] = 1 wt %, an increasing amount of small unilamellar vesicles forms, and in the samples below about 0.2 wt %, only vesicles are observed. The average radius of the vesicles [R] increases from about 90 Angstrom at 0.3 wt % to 110 Angstrom at 0.1 wt %. The transition from micelles to vesicles with decreasing surfactant concentration was also observed in the samples at [SDS]:[DDAB] = 90:10 in which, however, an additional amount of bilayer sheets was seen to be always present. Compared with the micelles at [SDS]:[DDAB] = 95:5, the micelles formed at [SDS]:[DDAB] = 90:10 were considerably longer (c approximate to 40 Angstrom), but with similar cross section dimensions, and the vesicles formed were seen to be somewhat larger than the corresponding aggregates at 95:5. The relative standard deviation sigma(R)/[R] of the (number-weighted) vesicle size distributions was in the range 0.2 < sigma(R)/[R] < 0.3.