A rotary thresher for a combine harvester including at least a first concave and a second concave, which may be rotated around a rotor to move to or from a threshing position or one or more of one or more resting positions. The concaves are mounted in a frame that is configured to rotate around the rotor such that the second concave moves during rotation from a first resting position to the threshing position while the first concave is moved from the threshing position to a second resting position.