Periodic ab initio Hartree-Fock calculations on molecular crystals using the CRYSTAL programs are increasingly common, but to date basis set choice for these calculations seems to have been dictated more by convention rather than an informed choice from numerous alternatives. This work compares the use of basis sets built on 6-21G and 6-31G molecular basis sets with one double-zeta alternative. We show that the use of unmodified DZP basis sets is not only routinely possible, but results in substantially smaller basis set superposition error in the estimation of lattice energies. Through atomic calculations we demonstrate that, in part, this can be attributed to inherent deficiencies in the 6-21G and 6-31G basis sets, namely the constraining of valence s and p exponents to be equal. The analysis also sheds some light on the frequently cited but often poorly understood numerical instabilities that occur in calculations on some molecular crystals with the 6-31G basis set.