We derive optimal two-stage adaptive group-sequential designs for normally distributed data which achieve the minimum of a mixture of expected sample sizes at the range of plausible values of a normal mean. Unlike standard group-sequential tests, our method is adaptive in that it allows the group size at the second look to be a function of the observed test statistic at the first look. Using optimality criteria, we construct two-stage designs which we show have advantage over other popular adaptive methods. The employed computational method is a modification of the backward induction algorithm applied to a Bayesian decision problem. © 2007 Elsevier B.V. All rights reserved.