A bicycle rim for carrying a tire. The rim includes a circumferential tire bed including first and second opposing edge regions a circumferential spoke face, and first and second side walls extending from the spoke face to the first and second edge regions, respectively. The first and second side walls include first and second side wall extensions radially extending from the first and second opposing side regions and terminating at first and second outer radial edges, respectively. Each of the first and second outer radial edges defining a maximum width that is at least 3.8 mm. The thickness of the first and second side wall extensions varies with respect to a central radial axis. The thickness of the first and second side wall extensions is greater at the first and second outer radial edges than at a location radially spaced from the first and second outer radial edges and adjacent to the first and second opposing end regions, respectively.