A method for operating a speed control system of a vehicle is provided. The method comprises detecting an occurrence of a slip event, of a step encounter event, or of both events at a leading wheel of the vehicle. The method also comprises predicting that the occurrence of the detected event(s) will occur at a following wheel of the vehicle. The method yet further comprises automatically controlling vehicle speed, vehicle acceleration, or both vehicle speed and acceleration in response to the detection, the prediction, or both the detection and prediction. A speed control system comprising an electronic control unit (ECU) configured to perform the above-described methodology is also provided.