The geometrical structure of pure SDS and DTAB surfactant micelles in the absence of added salt as well as its dependence on the concentration of NaBr have been investigated at 40 degrees C using small-angle neutron scattering (SANS). In contrast to previous SANS measurements on the same systems we have analysed the scattering data in the entire regime of scattering vectors that are relevant for determining the structure of the micelles. Our obtained results for pure surfactant micelles, as well as those of mixed catanionic micelles presented in a recent study, show somewhat unexpectedly that ordinary surfactant micelles are shaped as circular or elongated bilayers (tablets). Both SDS and DTAB micelles appeared to be disk-like in pure D2O and the corresponding data were best fitted with a model for (monodisperse) oblate ellipsoids of revolution with half axes a=12.0 Angstrom, b=20.3 Angstrom ([SDS]=1.0 wt.%) and a=12.4 Angstrom, b=21.6 Angstrom ([DTAB]=1.0 wt.%). The half axis b related to the disk radius increases in both cases with an increasing amount of added salt to about 23 Angstrom (SDS) and 24 Angstrom (DTAB) at [NaBr]=0.1 M and at about [NaBr]=0.2 M the SDS micelles become tablet-shaped, i.e. tri-axial ellipsoids with half axes a<b < c. For DTAB micelles the disk-to-tablet transition occurs between [NaBr]=0.5 and 0.7 M. As the amount of salt is further increased the micelles grow strongly with respect to length, but decrease slightly in width to about b=20 Angstrom (SDS) and b=22 Angstrom (DTAB) at [NaBr]=1.0 M. Half the thickness of the micelles varies only slightly with the solution state and is found to be about 75-90% of the fully extended hydrocarbon chain (=16.7 Angstrom). Hence, all elongated micelles appeared to have an elliptical cross section with an axial ratio 1.5 < b/a < 1.6. At [NaBr]=0.7 M the SDS micelles are considerably elongated and polydisperse and their (volume-weighted) average length increases rapidly with surfactant concentration from about 200 Angstrom at [SDS]=0.25 wt.% to about 400 Angstrom at [SDS]=1.0 wt.%. At [NaBr]=1.0 M the SDS micelles were seen to be shaped as long flexible ribbons too long, i.e. several thousands of Angstroms, for their size distribution to be determined from our SANS data whereas DTAB micelles still were rather short, i.e. c=30 Angstrom.