The primary objective of a phase II clinical trial of a new drug or regimen is to determine whether it has sufficient biological activity against the disease under study to warrant more extensive development. Such trials are often conducted in a multi-institution setting where designs of more than two stages are difficult to manage. This paper presents two-stage designs that are optimal in the sense that the expected sample size is minimized if the regimen has low activity subject to constraints upon the size of the type 1 and type 2 errors. Two-stage designs which minimize the maximum sample size are also determined. Optimum and "minimax" designs for a range of design parameters are tabulated. These designs can also be used for pilot studies of new regimens where toxicity is the endpoint of interest.