Poisson processes sometimes govern expts. in which the zero class is unobserved. The authors discuss maximum likelihood and moment methods of applying the truncated Poisson to such data. The moment method although less efficient is recommended since it involves fewer computations than the M. L. method. The truncated negative binomial, as an example of a compound Poisson process, is also examined. The authors recommend M. L. estimation in this case. No examples are given.