  Deterministic light-induced spin squeezing in an atomic gas is limited by
photon shot noise or, equivalently, by atomic state information escaping with
the light field mediating the effective atom-atom interaction. We show
theoretically that the performance of cavity spin squeezing [M.H.
Schleier-Smith, I.D. Leroux, and V. Vuleti\'{c}, Phys. Rev. A 81, 021804(R)
(2010)] can be substantially improved by erasing the light-atom entanglement,
and propose several methods for doing so. Accounting for light scattering into
free space, quantum erasure improves the scaling of cavity squeezing from
S^(-1/2) to S^(-2/3), where S is the total atomic spin.
