It is well known that the application of infinite-range interactions can generate massively entangled states with applications in quantum information and quantum metrology.  Combining recent exact solutions with a controlled perturbative calculation in the inverse system size, we analytically determine the spin-squeezing in Ising models with power-law (1/r^alpha) decaying interactions in D dimensions, thus extending the understanding of spin-squeezing into a much broader and experimentally relevant context.  When interactions are not infinitely long-ranged, the spin squeezing is generally modified by both a lack of translational invariance and by a departure from collective (i.e. within the Dicke manifold) dynamics.  In the large system limit, the former effect destroys squeezing for /any/ power law.  On the other hand, remarkably, the departure from collective dynamics has /no/ effect on squeezing in the large system limit for sufficiently long-range interactions (alpha<2D/3).