A faucet having a body (200) extending from forward to aft ends to define a body cavity, the body (200) includes an aft wall having faucet inlet ports, and a faucet outlet between the forward and aft ends; a push knob (120) coupled to the body forward end; a cartridge (270) fixed within the body cavity, the cartridge (270) has a cartridge cavity with an aft seal seat, a cartridge outlet port forward of the aft seal seat, and a cartridge inlet port aft of the aft seal seat; a piston (130) within the cartridge cavity, defining an aft seal lip: the piston (130) is movable by the push knob (120) from first to second positions, to move the lip and open the faucet; and the piston (130) moves from the second to the first positions, to position the lip against the aft seal seat and close the faucet; and a linear damper (135), mounted to the body forward end.