New 3D HCN quantitative J (QJ) pulse schemes are presented for the precise and accurate measurement of one-bond 15N1/9-13C1', 15N1/9-13C6/8, and 15N1/9-13C2/4 residual dipolar couplings (RDCs) in weakly aligned nucleic acids. The methods employ 1H-13C multiple quantum (MQ) coherence or TROSY-type pulse sequences for optimal resolution and sensitivity. RDCs are obtained from the intensity ratio of H1'-C1'-N1/9 (MQ-HCN-QJ) or H6/8-C6/8-N1/9 (TROSY-HCN-QJ) correlations in two interleaved 3D NMR spectra, with dephasing intervals of zero (reference spectrum) and approximately 1/(2J(NC)) (attenuated spectrum). The different types of 15N-13C couplings can be obtained by using either the 3D MQ-HCN-QJ or TROSY-HCN-QJ pulse scheme, with the appropriate setting of the duration of the constant-time 15N evolution period and the offset of two frequency-selective 13C pulses. The methods are demonstrated for a uniformly 13C, 15N-enriched 24-nucleotide stem-loop RNA sequence, helix-35psi, aligned in the magnetic field using phage Pf1. For measurements of RDCs systematic errors are found to be negligible, and experiments performed on a 1.5 mM helix-35psi sample result in an estimated precision of ca. 0.07 Hz for 1D(NC), indicating the utility of the measured RDCs in structure validation and refinement. Indeed, for a complete set of 15N1/9-13C1', 15N1/9-13C6/8, and 15N1/9-13C2/4 dipolar couplings obtained for the stem nucleotides, the measured RDCs are in excellent agreement with those predicted for an NMR structure of helix-35psi, refined using independently measured observables, including 13C-1H, 13C-13C and 1H-1H dipolar couplings.