A new technique is offered to determine the quantity of radioactive particles observed by a scintillation or proportional counter when the distribution of the source particles vs particle energy is immersed in the distribution of the background particles.The particle identification problem is interpreted from the point of view of a parameter estimation problem in mathematical statistics in the following way: Assume there areMevents, where an event is the occurrence of a scintillation counter pulse.Mis a known number,Nof these events are associated with the desired source particles and the scintillation counter output is source plus background. The remaining (M‐N) events consist of background alone. The background statistics are assumed known and the source pulse amplitude distribution is assumed known to withinKdistribution parameters. One number, the amplitude of the counter response, is observed for each of theMevents. The problem is to estimateN.There are (K+1) unknown parameters: the numberNand theKunknown parameters of the source pulse distribution. The problem is solved by what is essentially a method of moments technique. The estimation procedure has desirable statistical properties for largeNandMin that the estimate ofNis asymptotically unbiased and that the relative variance of the estimate ofNasymptotically goes to zero.Implementation of this technique supplants the conventional multichannel pulse‐height analyzer with digital recording of the individual pulse count amplitudes and subsequent data processing by a modest size digital computer.