The effect of complex sets of single- and double-level traps on deep level transient spectroscopy (DLTS) spectra is critically discussed using a numerical simulator. The simulation takes into account: the partial trap ionization, the effect of base doping, the dynamics of charged traps, and the depletion layer effect. The modeling of the capacitance transient has been extended when many traps are present. The simulator has been used for the analysis of DLTS spectra of platinum-doped and high-energy (12 MeV) electron-irradiated silicon diodes. These examples evidence how the simulation method increases the resolution of the DLTS technique. A detailed analysis of the emission kinetics of two energy level traps is also presented.