The micelles formed by sodium dodecyl sulfate (SDS) are studied in aqueous solutions at 294 K as a function of nominal SDS concentration (C) using positron lifetime spectroscopy. In a four-component analysis of the data, it appears that the lifetime (tau(3)) of the positronium triplet state (o-Ps) in the aqueous phase decreases significantly with increasing C. Preliminary results on sodium methanesulfonsate solutions show that this compound does not result in any significant Ps lifetime quenching. Thus, the changes in the lifetime are attributed to the trapping of Ps from the aqueous to the organic micellar phase, On the basis of simple diffusion-controlled kinetics, the observed linearity of 1/tau(3) with C indicates that the ratio of the micelle core radius (R(mic)) to the aggregation number (N-ag) is about constant over the concentration range investigated, in agreement with information from other studies. Quantitatively, on the hypothesis of a constant value of N-ag = 64, the use of the simple model, or of a more rigorous one, for Ps diffusion and trapping leads to R(mic) = 1.50 and 1.19 nm, respectively. Both values are lower than 1.84 nm as expected from other studies on the total SDS aggregate radius at 298 K. However, taking account of the size of the polar sulfate groups and of some slight variation of N-ag with C, the most complete model leads to R(mic) = 1.75 nm, in satisfactory agreement with the 1.84 nm value. Examination of the intensities of the two longest-lived components, related to o-Ps in the aqueous and micellar phases, shows that, as was the case for reverse micelles, most of the Ps formation occurs in the former. The aggregated SDS molecules display a very low inhibiting power toward Ps formation, with an inhibition constant of 0.01 M(-1), in agreement with the low ability of alkyl sulfates and sulfonates to scavenge electrons. The trapping of Ps in the micelles is confirmed by the continuous increase with C of the intensity of the longest-lived component, related to o-Ps in the organic phase.