The stabilizer works with any conventional cruise control (CC) and permits automatic CC in slower heavy traffic as it eliminates laborious frequent manual actuation of CC control buttons otherwise needed in such heavy traffic. More frequent automatic CC operation at slower speeds increases fuel efficiency. When the vehicle maintains a speed above a minimum speed and exceeds a brief preset period, the speed stabilizer sets the cruise control at that speed. When the cruise control is thus engaged, the driver's foot can move the accelerator pedal within a small tolerance range without canceling the cruise control. When the pedal is close to the bounds of the tolerance range, a warning signal such as a flashing LED display, is generated by the speed stabilizer to inform the driver that further movement of the pedal will cause acceleration/deceleration, automatically canceling cruise control. Actuation of conventional CC control buttons restores conventional CC.