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Short flow first scheduling (SFF) strategy is effective in obtaining more stringent performance bounds for short flows in Internet. However, previous strict SFF approaches invested the short flows with excessive preference leading to the starvation of other long flows. Moreover, these SFFs are hard to be deployed due to either extreme complexity or the modification of TCP protocol. Inspired by the fairness and practicality of deficit round robin (DRR), we proposed a novel scheduling mechanism, namely deficit round robin with short flow first (DRR-SFF), which improves the performance of short flows with limited penalizing long flows. DRR-SFF uses weighed DRR to schedule short and long flows respectively and treats long flows more fairly. Through trace-driven simulation, we show that the mean transmission time and loss rate of short flows under DRR-SFF are significantly reduced compared with FIFO scheduling using DropTail. Meanwhile, the performance of long flows under DRR-SFF does not degrade much, retaining to that of FIFO scheduling. Our results demonstrate DRR-SFF is superior to strict SFF approaches, as the latter drives long flows into starvation in our simulations. Moreover, DRR-SFF inherits the O(1) computation complexity of DRR, which makes it easy to be deployed in edge routers.