A mechanical timepiece oscillator comprising, between a first rigid support element directly or indirectly fixed to a plate, and a solid inertial element, a flexure bearing mechanism including at least two first flexible strips which support said solid inertial element and are arranged to return said solid inertial element to a rest position, wherein said solid inertial element is arranged to oscillate angularly in an oscillation plane about said rest position, said two first flexible strips do not touch each other and their projections onto said oscillation plane cross, in the rest position, at a crossing point (P), in proximity to which passes the axis of rotation of said solid inertial element perpendicularly to said oscillation plane, wherein said flexure bearing mechanism includes, superposed on each other, at least one upper level, which includes, between an upper support and said solid inertial element, at least one upper primary strip extending in a first upper strip direction (DL1S) and one upper secondary strip extending in a second upper strip direction (DL2S), crossed in projection at an upper crossing point (PS), and at least one lower level, which includes, between a lower support and said solid inertial element, at least one lower primary strip extending in a first lower strip direction (DL1I) and one lower secondary strip extending in a second lower strip direction (DL2I), crossed in projection at a lower crossing point (PI), wherein said upper level and said lower level each include, between said plate and said upper support, and respectively said lower support, a translational table comprising at least one elastic connection along one or two axes of freedom in the oscillation plane, and whose stiffness is lower than that of said upper level and also than that of said lower level, to allow a relative translation between said upper level and said lower level, in order to allow adjustment of the relative position of the two embedding points of said flexible strips on the side of said solid inertial element, and modification of the stiffness of said translational tables to allow adjustment of any anisochronism.