An overshoot suppression scheme to improve the performance of the digital Song adaptive delta modulator (DM) for picture transmission is described. This scheme allows for a faster increase in the step sizes than permitted by overshoot and settling time considerations, thus improving rise-time performance. The overshoot suppression (OSS) algorithm used has been verified using computer simulation on a PDP-8. Furthermore, experimental results using computer generated test pictures as well as pictures from a flying-spot scanner show the improvements due to the overshoot suppression scheme. It is also shown that the additional hardware required for the actual implementation of the algorithm is simpler than those encountered in the literature, and gives better signal-tracking accuracy. Upper bounds for the settling time, with and without OSS, are derived showing an improvement with the suppression scheme. Stability conditions are also derived permitting the proper selection of DM parameters.