The polarizabilities of the F - , Cl - and Br - ions in their soild lithium and salts in the four-coordinated B3 and eight-coordinated B2 phases are predicated from ab initio electronic structure computation. These results plus those for the experimentally observed B1 structure yield insights into the mechanisms by which the in-crystal environment modifies hablide p polarizabilities. T The anion polarizability in each B2 phase having the cation-anion separation of the B1 structure is reduced compared with that in the B1 phase by the overlap with eight cation neighbours rather than six, these polarizabilities being essentially identical in the corresponding point charge lattices. The greater equilibrium cation-anion separation R e in the B2 compared with the B1 phase causes each halide polarizability at its R e to be greater in the B2 phase than in the B1 material. These B2 phase polarizabilities can be accurately predicated from the same f function, which describes the dependence of the polarizability on R e for different salts having the B1 structure. This supplements previous evidence from the caesium halides that these anion polarizabilities are determined solely by R e, being insensitive to the precise disposition of the cation neighbours. The halide polarizabilities in the B3 phase are larger than those predicted by the above function describing the dependence of polarizability on R e. This phase thus differs from B1 or B2 materials, fluorite structured alkaline earth fluorides or MgF 2 in that the halide polarizabilities in the four latter are all essentially determined by R e through the same function. The halide polarizabilities in the B3 phase differ by exhibiting a specific structural dependence in addition to their R e variation. A new function describes the R e dependence of halide polarizabilities in the B3 phase.