A timepiece barrel assembly, including a barrel mainspring mounted between a barrel drum and a receiving surface of a barrel core coaxial to the drum. The spring is made of a multiphase, cobalt-nickel-chromium based alloy, having a Young's modulus of between 200 and 240 GPa and a shear modulus of between 80 and 100 GPa, and having a width to thickness ratio of between 9 and 21, and the maximum radius of the steel or stainless steel core relative to its pivot axis is less than nine times the maximum thickness of the spring, and the barrel assembly includes, on the spring or the drum, a mechanism limiting longitudinal clearance, towards the pivot axis, between the drum and the mainspring.