A new data processing mode for Fourier Transform Pulsed-Gradient Spin-Echo (FT-PGSE) data sets is described. Unlike conventional analysis methods, it uses all of the significant spectral information of a data set of typically 16 or 32 different magnetic field gradient settings for 10-1000 significant frequency channels out of a 1-16K FT-PGSE data set. The procedure is based on a global least squares minimization approach at two levels : an upper level that optimizes the actual global self-diffusion coefficient data and a lower one that optimizes the amplitude(s) of the component(s) for a particular frequency channel. This approach relies on the intrinsic property of FT-PGSE data sets in that the whole bandshape of a particular component attenuates by exactly the same relative amount upon incrementing the field gradient pulse parameters (Stilbs, P. Anal. Chem. 1981, 53, 2135 which was also shown to provide a pathway for separating the spin-echo bandshapes of the constituents of multicomponent systems. As a consequence of the coupled, global minimization approach of the method, the signal-to-noise ratio (S/N) of the FT-PGSE experiment is enhanced by typically a factor of 10 or more, since all of the available spectral information is utilized (effectively, a few 100 frequency channels/peak are combined). The present (global) optimization procedure (named CORE-NMR, COmponent-REsolved NMR spectroscopy) fundamentally differs from the diffusion-ordered spectroscopy procedure(s) introduced by Johnson et al., but the two approaches can be regarded as complementary. CORE-NMR is expected to find particular use in current studies on aggregation and binding in polymer and surfactant solutions, solving evaluation problems originating from the poor S/N, overlapping bandshapes, and high dynamic range with regard to relative constituent spectral intensities. Typically these difficulties are all present at the same time in such studies. CORE-NMR is equally well applicable to electrophoretic FT-NMR, where the signals of a particular component also vary coherently with an experimental parameter (the electrophoretic current) with regard to intensity and phase. As outlined, the generic CORE approach is of course also applicable to any other type of spectroscopic data, where individual intensities of separated or overlapping component spectral bandshapes decay/evolve in a similarly correlated manner as in, e.g., FT-PGSE NMR.