The convergence properties of counterpoise corrected hypersurfaces towards the limit of infinite basis set size within a specific method are discussed. In the case of concerted hydrogen exchange of the cyclic hydrogen fluoride trimer counterpoise correction is shown to be highly counterproductive for the convergence speed towards the basis set limit. A best estimate for the MP2 basis set limit of -15.2 kcal/mol for the stabilization energy and of 18.7 kcal/mol for the concerted hydrogen exchange barrier of the cyclic hydrogen fluoride trimer is deduced by calculations using basis sets up to aug-cc-pV5Z. Both results are very well predicted in the uncorrected case already with the smaller basis sets in the MP2/aug-cc-pVxZ series, whereas counterpoise correction completely fails to improve predictions mainly due to a wrong correction of the dynamic electron correlation contribution. Only with very large basis sets it is possible to obtain counterpoise corrected results of comparable quality.