A vehicle suspension control includes a vehicle body control responsive to body/wheel velocity at the corners of the vehicle body to derive a demand force command for dampers at each corner of the vehicle body for vehicle body control and applies each of the derived demand force commands to its respective damper only when a comparison of the direction of the demand force command with the sensed relative velocity of the damper indicates that a force corresponding to the demand force command can be effectively exerted by the damper. But the suspension control also includes a vehicle stability control responsive to an indicated vehicle lateral acceleration in a turn to determine, independently of the vehicle body control, a stability compression damping command for the suspension dampers on the side of the vehicle opposite the direction of the lateral acceleration and a stability rebound damping command for the suspension dampers on the side of the vehicle in the direction of the lateral acceleration. While the lateral acceleration is sensed, the vehicle stability control applies the stability compression damping command to the suspension dampers on the side of the vehicle opposite the direction of the lateral acceleration and the stability rebound damping command to the suspension dampers on the side of the vehicle in the direction of the lateral acceleration, without regard for the direction of demand force for any of the suspension dampers. The resulting stiffening of the suspension on the outside of the turning vehicle in compression and on the inside of the turning vehicle during rebound helps keep the tires of the vehicle firmly in contact with the road surface in spite of road surface irregularities.