[en] The ''low-beta insertions'' that are incorporated into most of the new storage ring designs result in very high values of beta in the strong quadrupoles near the interaction regions, and in large natural values of the average chromaticity, ξ = dν/dδ with ν the betatron wave number and δ = Δp/p. In the past the average chromaticity was controlled by the introduction of sextupole magnets into the ring lattice and it was only necessary to correct the linear portion of the betatron tune shift with momentum deviation. In the design of recent storage rings, however, it has become necessary to correct the non-linear terms of the tune shift with momentum deviation. The purpose of this paper is to present analytic formulae for the small-amplitude betatron tune shift with momentum through cubic terms in the momentum deviation. 5 refs