A group-sequential design for clinical trials that involve treatment selection was proposed by Stallard and Todd (Statist. Med. 2003; 22:689-703). In this design, the best among a number of experimental treatments is selected on the basis of data observed at the first of a series of interim analyses. This experimental treatment then continues together with the control treatment to be assessed in one or more further analyses. The method was extended by Kelly et al. (J. Biopharm. Statist. 2005; 15:641-658) to allow more than one experimental treatment to continue beyond the first interim analysis. This design controls the familywise type I error rate under the global null hypothesis, that is in the weak sense, but may not strongly control the error rate, particularly if the treatments selected are not the best-performing ones. In some cases, for example when additional safety data are available, the restriction that the best-performing treatments continue may be unreasonable. This paper describes an extension of the approach of Stallard and Todd that enables construction of a group-sequential design for comparison of several experimental treatments with a control treatment. The new method controls the type I error rate in the strong sense if the number of treatments included at each stage is specified in advance, and is indicated by simulation studies to be conservative when the number of treatments is chosen based on the observed data in a practically relevant way.