An annular assembly for compressing a seat of a ball-valve, including: a valve body or insert, including an annular internal counter-bore that defines an inner counter-bore diameter; a sleeve inserted into the annular internal counter-bore, defining at least one outer diameter of the sleeve; the body or the insert defining with the sleeve an annular housing in which the assembly includes, in succession: a downstream stack of head rings, an annular head shim, a stack of mechanisms of compression, an annular base shim, and an upstream stack of base rings.