The coupling between improvement of the basis set and the valence electron correlation method has been studied quantitatively for the total atomization energies (TAEs) of a number of small molecules, using basis sets of up to [7s6p5d4f3g2h/5s4p3d2f1g] quality. Very significant coupling is found to exist. Using a scaled basis set extrapolation beyond [6s5p4d3f2g/4s3p2d1f] at the MP2 or CCSD level, mean absolute errors of 0.18 and 0.15 kcal/mol, respectively, can be obtained for the TAEs of a number of small polyatomic molecules, compared to 0.12 kcal/mol using CCSD(T) throughout.