This paper is concerned with maximum likelihood estimation of the Poisson parameter λ when the zero class has been truncated and when errors of observation have resulted in eliminating some though not necessarily all of the one class. Estimators are derived both for λ and the proportion θ of ones eliminated as a consequence of faulty observation. A table and a graph of the estimation function involved are given. Asymptotic variances and covariances of the estimators are derived, and a table of the variance function applicable in calculatingV(λ) is given. An illustrative example is included.