Conductivities and dielectric constant measurements in water at 25 degrees C have been made on the amphiphilics sodium n-dodecyl sulfate, n-dodecyltrimethylammonium bromide, and chlorpromazine hydrochloride. By using the conductivity/concentration data, critical micelle concentrations (cmc) have been determined by applying the Williams definition and two forms of the Phillips method. This first Phillips form consists of an approximation to Gaussians of the second derivative of the conductivity/concentration data followed by two consecutive integrations. The second form, which is proposed here, consists of the application of a combination of the Runge-Kutta numerical integrations method and the Levenberg-Marquardt least-squares fitting algorithm. The proposed method permits the determination of the cmc in systems with low aggregation numbers and with slow variations of physical property/concentration curves allowing the determination of the so-called second cmc. A comparative study with results obtained by dielectric constant measurements has been carried out. With this new technique, the cmc＇s (first and second) are directly obtained as singular points in the dielectric constant/concentration curves, and thus, this technique is an alternative to the determination of cmc＇s from conductivities.