Full configuration-interaction calculations for BH, HF, and CH3 are used as benchmarks for determining the accuracy of summation approximants for CCSD(T) coupled-cluster theory and fourth-order Moller-Plesset perturbation theory as function of bond distances. A continued-fraction approximant [the CCSD(T)-cf method] reliably improves CCSD(T). The MP4-qlambda procedure, in which repartitioned perturbation theory is summed with a quadratic approximant, is much more accurate than conventional MP4 but more sensitive to bond stretching than is CCSD(T)-cf. Diagnostics for estimating the accuracies of the methods, based on singularity analysis of perturbation series, are developed and discussed. (C) 2002 Elsevier Science B.V. All rights reserved.