We consider a system with two heterogeneous traffic classes. The users from both classes randomly generate service requests, one class having light-tailed properties, the other one exhibiting heavy-tailed characteristics. The heterogeneity in service requirements reflects the extreme variability in flow sizes observed in the Internet, with a vast majority of small transfers ("mice") and a limited number of exceptionally large flows ("elephants"). The active traffic flows share the available bandwidth in a Processor-Sharing (ps) fashion. Theps discipline has emerged as a natural paradigm for modeling the flow-level performance of band-width-sharing protocols liketcp. The number of simultaneously active traffic flows is limited by a threshold on the maximum system occupancy. We obtain the exact asymptotics of the transfer delays incurred by the users from the light-tailed class. The results show that the threshold mechanism significantly reduces the detrimental performance impact of the heavy-tailed class.