A method for controlling the speed of internal combustion engines in heavy duty trucks and the like compensates for the overshoot, i.e., the difference between a targeted or commanded engine speed and a transient overspeed or underspeed. The method comprehends executing a program or subroutine where a throttle or engine speed change command is received by a controller, the engine speed change is monitored, a value of overshoot (on both an engine speed increase or decrease) is detected and the detected overshoot is subsequently utilized to temporarily reduce the speed change command, thereby effectively eliminating the overshoot and more positively and quickly arriving at the targeted engine speed.