We consider a system with a dispatcher and several identical servers in parallel. Task processing times are known upon arrival. We first study the impact of the local scheduling policy at a server. To this end, we study random routing followed by a priority scheme at each server. Our numerical results show that the performance (mean waiting time) of such a policy could be significantly better than the best known suggested policies that use FCFS at each server. We then propose to use multi-layered round robin routing, which is shown to further improve system performance. Our analysis involves a combination of comparing analytic models, heavy traffic asymptotic and numerical work.