The microsolvation of Li+ by both argon and krypton atoms has been studied based on a new potential energy surface that includes two- and three-body interactions; the potential terms involving the lithium ion were calibrated with CCSD(T)/aug-cc-pVQZ energies after being corrected for the basis-set superposition error. The structures of the Li+ArnKrm (n + m <= 20) clusters arising from global optimization show a first solvation shell preferentially occupied by krypton atoms. These binary-solvent microsolvation clusters are most stable when the total number of krypton (argon) atoms occupy the first (second) solvation shell.