The axillary piece (20) is designed for incorporation within an item of clothing in the region beneath the bra of a generally oblong form, with a longitudinal plane of symmetry (L) and a transverse plane (D) designed to essentially reach to below the armhole and to both sides of said transverse plane (D), a front part (25) designed to come beneath the panel forming the arms of the article and a rear part (26) designed to come beneath the part forming the bust of the article. Furthermore said piece has a three-dimensional configuration without ribs wherein at least laterally in the immediate region of the transverse plane (D), the front (25) and rear parts (26) form two relief wings (30,31), each essentially shaped as a section of a cone the summit of which is essentially at the intersection (24) of eh longitudinal (L) and transversal planes (D).