A valve mount for water saving core shaft of a single-handled faucet has a valve embodiment housed in a receiving cavity of a faucet body with the upper section provided with internal threads to be in locking engagement with a locking cap. In the valve chamber of the valve embodiment are housed sequentially a rotary member, a switch stick, a regulation seat and a discharge control valve. The inner periphery of the valve chamber is provided with a plurality of retaining recesses corresponding to the spring plates defined on the rear cavities of the rotary member and the engaging teeth of the regulation seat are in engagement with the spring plates on the right and left recess of the rotary member. On the upper section of the rotary seat are provided with outer teeth which are engaged with the inner teeth of a stop member. The upper end of the switching stick is secured a faucet handle whereby the handle of such a faucet can be move up and also to the right or left in a step-like manner to precisely control the minimum outlet of cold and hot water without worrying the sudden massive discharge of water due to an improper actuation of the handle, resulting in the effective use of water.