An improved method for the analysis of multi-exponential transients with high resolution has been applied to DLTS. Full-waveform fittings, using the technique of Modulating Functions, are made to digitized transients captured by a computer. This technique is described and results for both simulated data (with noise) and real data are shown. The advantages over previously published techniques in resolution, calculation speed, insensitivity to truncation error and noise are discussed. Also, how this method allows for a determination of the number of components is presented.