Consider a Bernoulli population, with p denoting the proportion of units possessing attribute A. Based on one-at-a-time sampling from this population, we want to make a decision as to whether (the unknown) p is small or large, according to the following specifications. Suppose 0<p1<p2<1. We let a* denote the desired probability of erroneously not deciding that p is small, when in fact p = p1. Likewise we let B* denote the desired probability of erroneously not deciding that p is large, when in fact p = p2. Two tests (i.e., decision rules) designed to meet these specifications approximately are: (1) the sequential probability ratio test (SPRT) (Wald 1947), which approximately minimizes "average sample number" (ASN) if in fact p = p1 or p = p2; and (2) the 2-SPRT (Lorden 1976), which helps to reduce ASN for values of p intermediate between p1 and p2.