A rim structure for a bicycle wheel that includes, at its periphery, an annular channel designed to receive a tire, such channel being demarcated by an upper bridge devoid of openings with the exception of the valve opening, and two lateral flanges, such flanges having end butts for gripping the tire. The upper bridge has a narrow and recessed central rim well demarcated by a base and two lateral walls, the rim well being bordered by two bead seats that are oblique from the rim well towards the flanges. The invention is also related to a wheel having such a rim and a wheel equipped with a tire mounted without an air tube and having such a rim.