A standard problem of hypothesis testing and quality control requires a sampling plan for which the OC is at least 1 – α0if a parameter θ assumes the value θ0and is no more than β1if θ = θ1> θ0. The efficient procedure for obtaining such a plan with minimum sample size by using available tables has been described by Guenther [1]. When items are sampled one at a time, these procedures can be modified so as to quit sampling when the decision is obvious. Patil [5, 6] briefly discussed such plans for the binomial case. This paper contains not only a thorough discussion of the binomial case but includes the companion hypergeometric case as well, together with examples.