The dielectric properties of dodecyldimethylamine oxide [DDAO] in salt-free aqueous solutions under different pH conditions have been measured in the frequency range from 400 kHz to 100 MHz. DDAO is an amphyphile that may exist either in a neutral or a cationic protonated form, depending on the pH of the aqueous solution. This condition realizes, above the cmc, ionic or nonionic micelles in an easily controlled way. While the dielectric response of a neutral micelle, in the low-concentration limit, is rather flat, a dielectric dispersion occurs at pH values lower than pH = 7. This dielectric dispersion is attributed to an orientational polarization mechanism of the entire micelle, in addition to the usual Maxwell-Wagner effect. This orientational polarization is due to an electric dipole moment induced by protonation of the micellar surface. The average size of the micelle, considered as a rigid sphere of radius R-H, has been evaluated from the relaxation time of the observed dielectric relaxation. We found that R-H decreases with the increasing of the micellar ionization induced by acidic pH values. To obtain an independent evaluation of the micelle size, we have performed dynamic light-scattering experiments. These results are in a reasonable agreement with those derived by dielectric measurements. The influence of the ionic counterion species on the micelle size is briefly discussed.