The present invention comprises a new and improved adjustable rear sight for firearms which comprises a polymer sight body and a metal aperture screw which is adjustable for elevation by screwing the aperture screw up or down in a threaded insert which is inserted in a cavity which extends from an upper surface to a lower surface of the sight body. The polymer sight is held securely in a sight mounting dovetail via a flex plate which is held to the bottom of the sight body by a flange on the bottom end of the threaded insert. The flex plate is sized to fit tightly in the sight mounting dovetail.