Summary: We investigate the power of the Kolmogorov-Smirnov test for negativity of signals in signal detection problems with Brownian motion noise. Strict unbiasedness and admissibility are established. Moreover, taking up an approach of {\it J. Hájek} and {\it Z. Šidák} [Theory of rank tests. (1967; Zbl 0161.381)] for the classical Brownian bridge case, we compute the directional derivative of the power function at the hypothesis, thus obtaining the principal direction of alternatives of the test. As an application, in a hazard rates set-up, one-sided Rényi-tests may be adjusted by choosing their weight function such that they are most sensitive against a prescribed type of alternatives. Finally, we give some numerical and simulation results.