In the original two-stage method of group-testing, it is well known that ifpis the proportion of infected individuals in the population, then the optimal group size is approximatelyp−1/2whenpis small. A modified mathematical treatment of the problem is used in this paper to show that for allp< .3 the optimal group size is either 1 + [p−1/2] or 2 + [p−1/2], where [x] denotes the integer part ofx, and, when the optimal group size is used, the expected number of tests per individual is between 2p1/2–p/2 and 2p1/2+ 4p3/2. Other interesting features of the two-stage method, as a function of group size, are also revealed.