The changes in size and shape of micelles formed in a 0.2 mol dm(-3) sodium dodecyl sulfate (SDS) aqueous solution are studied as a function of added I-pentanol concentration at 294 K, by using positron annihilation lifetime spectroscopy (LS). As in a previous work, the trapping of ortho-positronium (o-Ps) from the aqueous to the organic micellar subphase results in the appearance of two o-Ps states with distinct lifetimes. The LS data are analyzed on the basis of a time-dependent trapping rate coefficient, which involves two parameters characteristic of the micellar system: the mean core radius, R-core, and the mean aggregation number, N-ag. Setting the N-ag values from a previous experimental work, the LS data give thus access to R-core. In parallel to the variation of N-ag, R-core is found to decrease slightly, then to increase steadily as the alcohol concentration is increased. A quantitative agreement is found between the experimental values of R-core and those expected on the basis of the volume of the hydrocarbon tails of both SDS and I-pentanol with different geometries, strongly suggesting that the micelles evolve from spherical to rod shaped. In addition, the lifetime (tau (4)) Of those o-Ps atoms trapped in the micelles shows an initial increase, at low alcohol concentration, which is attributed to a decrease in the local surface tension inside the dodecane pools due to the presence of the shorter 1-pentanol hydrocarbon tail. On adding more alcohol, tau (4) shows a somewhat linear decrease, indicating a deeper penetration of the pentanol molecules inside the micelles with a resulting increase in their surface tension.