We investigate a way one can achieve good spectral resolution in 2H MAS NMR experiments. The goal is to be able to distinguish between and study sites in various deuterated materials with small chemical shift dispersion. We show that the 2H MAS NMR spectra recorded during a spin-relaxation experiment are amenable to spectral decomposition because of the different evolution of spectral components during the relaxation delay. We verify that the results are robust by global least-square fitting of the spectral series both under the assumption of specific line shapes and without such assumptions (COmponent-REsolved spectroscopy, CORE). In addition, we investigate the reliability of the developed protocol by analyzing spectra simulated with different combinations of spectral parameters. The performance is demonstrated in a model material of deuterated poly(methacrylic acid) that contains two 2H spin populations with similar chemical shifts but different quadrupole splittings. In 2H-exchanged cellulose containing two 2H spin populations with very similar chemical shifts and quadrupole splittings, the method provides new site-selective information about the molecular dynamics.