A bicycle wheel basically has a hub, a plurality of spokes extending outwardly from the hub and an annular rim coupled to the outer ends of the spokes for supporting a tire. The annular rim has a spoke attachment portion with a plurality of openings and radially extending recesses for receiving the outer end portions of the spokes therein. The outer end portions of the spokes are at least partially recessed within the radially extending recesses to provide an aerodynamic design. The outer end portions of the spokes are preferably bent such that first sections of the spokes are offset from sections of the spokes. These bends are positioned in the openings of the rims to retain the outer ends of the spokes in the openings of the rim. In selected embodiments, the offset section between the first and second sections is either thicker or corrugated.