Usually, efficient self-timed adders are realized using the dynamic differential cascode voltage switch logic. This allows the end-completion to be easily detected, but it makes circuit design and testing very complex, compelling the production of full-custom layouts and leading to a very long time before marketing. This paper presents a new 56-bit high-speed self-timed adder realized with conventional AMS 0.35 mm CMOS standard cells. The proposed circuit uses overlapped execution circuits, which exploit the initialization time that always elapses between two consecutive addition operations. Compared to several self-timed adders existing in the literature, the addition circuit proposed here shows brilliant advantages in terms of speed-performance, silicon area occupancy and power dissipation.