A method (and apparatus) for NMR relaxation measurements on borehole materials (e.g., drill cuttings, sidewall cores and whole cores) is based on combining an FID signal and spin-echo signals to obtain relaxation properties of a sample having fast relaxation components. The method comprises acquiring NMR signals from the sample, acquiring calibration NMR signals and acquiring a background signal (e.g., ringing after an excitation pulse). The background signal may be acquired using an additional static magnetic field to substantially spoil the NMR excitation volume in the sample. The acquired signals are processed to obtain a nuclear magnetic resonance relaxation property of the sample with at least one (first point) on the relaxation data produced from the FID and with the background data eliminated from the relaxation data.