We are interested in this work in studying the performances of static scheduling policies in presence of on-line disturbances. In the general case, the sensitivity of the schedules, i.e., the degradation of the performance of the solution due to the disturbances, is linear in the magnitude of the perturbation. Our main result within this paper is to show that in some scheduling contexts, namely the case of independent tasks, the sensitivity can be guaranteed not to exceed the square root of the magnitude of the perturbation.