Both the SCF and MP2 basis set superposition error (BSSE) calculated around a molecule of HF are strongly distance-dependent but nearly isotropic, with the highest degree of unsaturation centered along the HF bond. The secondary BSSE ( in the dipole moment), on the other hand, is highly anisotropic with larger effects identified near the F atom. Calculations on H3N-HF indicate that some cancellation may occur between the secondary BSSEs of the two subunits but that nonetheless, correction of this error is important in forming a proper picture of electronic rearrangements in molecular complexes.