More than 20 weighting functions proposed for DLTS are critically compared. It is shown that the variety of DLTS peak widths of different weighting functions was primarily due to the variety of shapes of the high-temperature side of the peak. A refinement of the classification scheme of the weighting functions is proposed. It is shown that the high-temperature side of the DLTS peak can be made independent of the weighting function, by considering the delay time between the end of the filling pulse and the beginning of the weighting function as an integral part of each weighting function. An optimum delay time (specific for each weighting function) is obtained by maximizing the figure of merit defined as the signal-to-noise ratio of the correlator divided by the DLTS peak width. Using the concept of optimum delay time, the functions can be classified into several groups according to their selectivity. The functions from one group differ only by their sensitivity, making it easy to select the functions with the best signal-to-noise ratios. In the second part of the paper, several misunderstandings concerning exponential correlators and double boxcars that frequently appear in the literature are revealed.