The abilities of several large Gaussian basis sets in conjunction with standard correlation treatments to reproduce the classical barrier to inversion in ammonia are compared and dissected. The basis sets incorporate primitive functions from five different sources. Second- and third-order Moller-Plesset perturbation theory and coupled-cluster methods have been used, with an extrapolation to the correlation limit taken from the literature. Each of the employed sets of primitive sp functions are found to be sufficient for 30 cm(-1) accuracy, but only after the inclusion of standard diffuse sp functions on nitrogen. Contraction errors in the basis sets are usually small, generally contributing less than 30 cm(-1) to the barrier height but up to 70 cm(-1) in some cases. An analysis of the basis set requirements for the accurate computation of core correlation has also been performed. It is found that, for sufficiently large basis sets, liberation of the Is electrons of nitrogen in the correlated treatments consistently results in reductions of 40-70 cm(-1) in the barrier height, even without the addition of core-specific functions to the standard basis sets. The best estimate of the classical inversion barrier in ammonia is 1821 cm(-1), with an estimated uncertainty of +/-30 cm(-1).