The solvation of fluoride and chloride anions (F- and Cl-, respectively) by water has been studied using effective fragment potentials (EFPs) for the water molecules and ab initio quantum mechanics for the anions. In particular, the number of water molecules required to fully surround each anion has been investigated. Monte Carlo calculations have been used in an attempt to find the solvated system X-(H2O)(n) (X = F, Cl) with the lowest energy for each value of n. It is predicted that 18 water molecules are required to form a complete solvation shell around a Cl- anion, where "complete solvation" is interpreted as an ion that is completely surrounded by solvent molecules. Although fewer water molecules may fully solvate the Cl-anion, such structures are higher in energy than partially solvated molecules, up to n >= 18. Calculations on the F- anion suggest that 15 water molecules are required for a complete solvation shell. The EFP predictions are in good agreement with the relative energies predicted by ab initio energy calculations at the EFP geometries.