A tip structure for a turbine blade comprises a tip surface of an airfoil that extends from a leading edge to a trailing edge and from a pressure side to a suction side of the airfoil. A suction side rail protrudes from the tip surface and comprises: a trailing portion extending flush with the suction side of the airfoil from an origination location at or near the trailing edge to an intermediate location on the suction side; and a leading portion extending from the intermediate location across the tip surface so as to create a suction side shelf region between the leading portion of the suction side rail and the suction side of the airfoil. A pressure side rail protrudes from the tip surface and comprises: a trailing segment extending flush with the pressure side of the airfoil from an origination location at or near the trailing edge to a middle location on the pressure side; and a leading segment extending from the middle location across a camber line on the tip surface so as to create a pressure side shelf region between the leading segment of the pressure side rail and the pressure side of the airfoil.