The invention relates to a timepiece component (1) that has an aperture (7) for receiving a support element (3) and includes a clamping system (13) for exerting radial force, enabling said timepiece component to be secured to said support element. According to the invention, the clamping system (13) includes a radial clamping device (15) that has a crown (6) for exerting said radial force and a concentric, blind recess (8) spaced apart from said aperture, to allow a travel for the crown. Moreover, the clamping system (13) further includes a device allowing a travel (17) that has a second, concentric, blind recess (10), spaced apart from said first blind recess (8), and located on the opposite surface to said first recess, to allow said crown a greater degree of freedom relative to said support element.The invention concerns the field of timepieces.