A balance set for a timepiece, with inertia adjustment for adjusting inertia and/or balancing and/or oscillation frequency of the balance, with a balance including an insert inserted into a recess of a felloe connected to a hub by a joining surface. The balance includes on the felloe thereof an elastic holding mechanism including two antagonistic elastic lips which, when stressed, allow insertion of the insert into the recess and which, when released, prevent removal of the insert from the recess. A sprung balance or a timepiece can incorporate such a balance.