Abstract: A bicycle rear wheel suspension which pivots a rear frame (10) behind the bottom bracket shell (5). The overall pivot width is greater than that of the bottom bracket shell (5), this ensures high torsional control and simplifies manufacture. At the junction of the seat stays (9) there projects a suspension housing (16) which sleeves axially or near axially over the stay runner (17). Both the suspension housing (16) and stay runner (17) feature flat sides to which bearing surfaces (19) are affixed. Between the bearing surfaces (19) there are needle roller bearing groups (20). One or both of the bearing surfaces (19) have deformable backs (21). The stepload slot (32) exerts a stepload force on the stepload pin (23) and the suspension such that only a bump loading force above that threshold stepload force would produce suspension movement. A hollow shock absorber (26) surrounds both the suspension housing (16) and stay runner (17).