There is a controversy in the literature concerning the use of one- and two-sided tests in clinical trials. Some contend that, when the research question relates to improved efficacy or safety, that is, the expected change is in one direction only, the hypothesis test should reflect this by being one-sided. Others insist on the use of a two-sided test in case a treatment difference in the opposite direction to that expected might turn up. We propose an alternative procedure to the two-sided test which also provides protection against overlooking a negative effect. The proposed procedure tests simultaneously for a positive difference and for equivalence. We illustrate the procedure by applying it to the results of a recent clinical trial.