A high-volume sprinkler head includes a barrel with a nozzle; a fixed portion and a relatively movable portion adapted for pivoting movement relative to the fixed portion. The barrel is mounted on an upper support base rotatable on a lower stationary base in opposite directions through an arc about a vertical axis. A fluid-operated actuator pivots the relatively movable portion of the barrel relative to the fixed portion of the barrel between first and second reaction angles that cause the barrel and the annular upper support base to rotate in opposite directions, about the substantially vertical axis, respectively, when a stream is emitted from the nozzle. A three-way valve in combination with adjustable stops on the stationary base may be used to pilot the actuator, with the adjustable stops determining the arcuate extent of the rotational movement of the sprinkler head.