This work describes how new methods for measuring one-bond, two-bond and three-bond heteronuclear and homonuclear residual dipolar couplings (RDCs) and 31P chemical shift anisotropy (31P CSA) values in RNA molecules of average size have been developed, facilitating the efficient, accurate and precise collection of these previously under-exploited but potentially powerful types of NMR structural constraints. These new methods for measuring RDCs and 31P CSA values have been developed using a 24 nucleotide hairpin derived from helix-35 of the 23S rRNA of E. coli, containing the psi746 modification, as a model molecule. A very large body of these types of NMR constraints has been carefully measured for helix-35psi746 using the novel methods. The residual dipolar coupling constraints can be implemented in structure calculations of RNA molecules, although the resultant structures must be interpreted with caution especially when RDCs from dynamic regions are included. The first round of structure calculations for helix-35psi746 has shown that the RDC constraints measured can have a dramatic impact on improving the quality of this RNA structure.