The counterpoise correction (CP) for the basis set superposition error (BSSE) for multimolecular aggregates can (in principle) be calculated by several different procedures, which give significantly different results. Three of these procedures arc discussed and illustrated with the HF...(HF)n...HF H-bonding aggregate. The three methods are (a) proceeding as if a dimer were formed between a unit of HF added to the H end of the growing aggregate, (b) as above, but with the HF being added to the F end, and (c) using the difference between the calculated CPs for the two aggregates before and after addition of the last HF, where the CPs for each aggregate are calculated using each monomeric unit in each aggregate with the ghost orbitals of all the other monomers. To separate the coupled effects cf BSSE and geometric optimization, the calculations were carried out on structures with both fixed and optimized H-F and F...H distances. Calculations were performed using the 6-31G, 6-31G(d), and 6-31G(d,p) basis sets at both the Hartree-Fock and MP2 levels. The significant differences in both the values and the trends of the CPs calculated by the different methods illustrate the need to use caution when applying the CP correction.