A multislice NMR imaging pulse sequence capable of measuring both the reversible and irreversible contribution to the transverse-relaxation rate (R'2 and R2) in a single scan is described. The method, termed GESFIDE (gradient-echo sampling of FID and echo) is based on sampling the descending and ascending portions of a Hahn echo with a train of gradient echoes. R2 and R'2 are computed by exploiting the differential evolution of the transverse magnetization before and after the phase-reversal pulse. Salient features of the method are its insensitivity to RF pulse imperfections and its high precision and efficiency. Applications examined involve the characterization of magnetically inhomogeneous tissues and biomaterials such as trabecular bone marrow in the skeleton and brain iron.