A magnetic recoil spectrometer (MRS) has been built and successfully used at OMEGA for measurements of down-scattered neutrons (DS-n), from which an areal density in both warm-capsule and cryogenic-DT implosions have been inferred. Another MRS is currently being commissioned on the National Ignition Facility (NIF) for diagnosing low-yield tritium-hydrogen-deuterium implosions and high-yield DT implosions. As CR-39 detectors are used in the MRS, the principal sources of background are neutron-induced tracks and intrinsic tracks (defects in the CR-39). The coincidence counting technique was developed to reduce these types of background tracks to the required level for the DS-n measurements at OMEGA and the NIF. Using this technique, it has been demonstrated that the number of background tracks is reduced by a couple of orders of magnitude, which exceeds the requirement for the DS-n measurements at both facilities.