Orbitals normally assigned to H or F atoms within the context of the 6-31G∗ or 6-31G∗∗ basis sets are centered at several different positions in the vicinity of a HF molecule and the basis-set superposition error (BSSE) calculated as the energy lowering engendered in HF. For ghost orbitals of either H or F type, the outer valence shell is responsible for the bulk of the total BSSE at either the SCF or MP2 level. The contribution of polarization functions is highly sensitive to the value chosen for the orbital exponent; the BSSE varies from nearly negligible for large exponents (the typical result of energy-based optimization) to values larger than the valence-shell contribution for more diffuse functions. Similar observations apply to perturbations of the monomer dipole moment which give rise to one element of secondary BSSE.