  This paper presents a systematic study of applying composite method
approximations with locally dense basis sets (LDBS) to efficiently calculate
NMR shielding constants in small and medium-sized molecules. The pcSseg-n
series of basis sets are shown to have similar accuracy to the pcS-n series
when n $\geq1$ and can slightly reduce compute costs. We identify two different
LDBS partition schemes that perform very effectively for density functional
calculations. We select a large subset of the recent NS372 database containing
290 H, C, N, and O shielding values evaluated by reference methods on 106
molecules to carefully assess methods of the high, medium, and low compute
costs to make practical recommendations. Our assessment covers conventional
electronic structure methods (DFT and wavefunction) with global basis
calculations, as well as their use in one of the satisfactory LDBS approaches,
and a range of composite approaches, also with and without LDBS. Altogether 99
methods are evaluated. On this basis, we recommend different methods to reach
three different levels of accuracy and time requirements across the four nuclei
considered.
