The NMR spectra of nucleic acids suffer from severe peak overlap, which complicates resonance assignments. 4D NMR experiments can overcome much of the degeneracy in 2D and 3D spectra; however, the linear increase in acquisition time with each new dimension makes it impractical to acquire high-resolution 4D spectra using standard Fourier transform (FT) techniques. The filter diagonalization method (FDM) is a numerically efficient algorithm that fits the entire multi-dimensional time-domain data to a set of multi-dimensional oscillators. Selective 4D constant-time HCCH-COSY experiments that correlate the H5–C5–C6–H6 base spin systems of pyrimidines or the H1′–C1′–C2′–H2′ spin systems of ribose sugars were acquired on the 13C-labeled iron responsive element (IRE) RNA. FDM-processing of these 4D experiments recorded with only 8 complex points in the indirect dimensions showed superior spectral resolution than FT-processed spectra. Practical aspects of obtaining optimal FDM-processed spectra are discussed. The results here demonstrate that FDM-processing can be used to obtain high-resolution 4D spectra on a medium sized RNA in a fraction of the acquisition time normally required for high-resolution, high-dimensional spectra.