This paper suggests two directional multivariate tests that aim at establishing superiority of a treatment over a control in at least one of several endpoints that are assumed to have a multivariate normal distribution. One of these tests is a one-sided, scale-invariant version of the classical Hotelling T2-test. The other is based on a summary score with weights derived from the data. Both tests overcome an important shortcoming of previous “one-sided” multivariate suggestions, namely that the null hypothesis was restricted to a single point in the multidimensional parameter space. The derivation of the tests is supplemented by simulations investigating their performance and by the application in an osteoporosis trial.