We extend our noniterative local correlation method [P. E. Maslen and M. Head-Gordon, Chem. Phys. Lett., 287, 102 (1998)] by defining a hierarchy of local spaces, ranging from small to large. The accuracy of the local method is then examined as a function of the size of the local space. A medium size local space recovers 98% of the MP2 correlation energy, and reproduces fine details of the potential energy surface such as rotational barriers with an RMS error of 0.2 kcal/mol and a maximum error of 0.4 kcal/mol. A large local space recovers 99.5% of the correlation energy and yields rotational barriers with a RMS error of 0.05 kcal/mol and a maximum error of 0.1 kcal/mol, at significantly increased computational cost.