The size and shape of the aggregates in the homogeneous isotropic micellar phase of the binary system ammonium perfluorooctanoate/heavy mater (APFO/D2O) have been extensively investigated by small- and wide-angle X-ray scattering, optical polarizing microscopy, self-diffusion NMR, and electrical conductivity techniques, as a function of temperature and surfactant concentration. The experimental results strongly suggest that there is a change in the structure of the micellar aggregates where the micelles undergo a shape transition, changing from spherocylinder (rod-shaped), at low surfactant concentration (W-A < 26 mt % APFO), to disk-shaped micelles (oblate ellipsoids), at high surfactant concentration (W-A > 28 wt % APFO).