We present a new method for scheduling independent tasks on a parallel machine composed of identical processors. This problem has been studied extensively for a long time with many variants. We are interested here in designing a generic algorithm in the on-line non-preemptive setting whose performance is good for various objectives. The basic idea of this algorithm is to detect some problematic tasks that are responsible for the delay of other shorter tasks. Then the former tasks are redirected to be executed in a dedicated part of the machine. We show through an extensive experimental campaign that this method is effective and in most cases is closer to some standard lower bounds than the base-line method for the problem.