Today's cellular systems operate under diverse resource constraints: limited frequency spectrum, network processing capability, and handset battery life. We consider a novel and important factor, handset screen status, i.e., whether the screen is on or off, which was ignored by previous approaches for optimizing cellular resource utilization. Based on analyzing real smartphone traffic collected from 20 users over five months, we find that off-screen traffic accounts for 58.5% of the total radio energy consumption although their traffic volume contribution is much smaller. Such unexpected results are attributed to the unique cellular resource management policy that is not well understood by developers, leading to cellularunfriendly mobile apps. We then make a further step by proposing screen-aware optimization, by leveraging the key observation that screen-off traffic is much more delay-tolerant than its screenon counterpart due to a lack of user interaction. Our proposal can better balance the key tradeoffs in cellular networks. It saves up to 60.92% of the network energy and reduces signaling and delay overhead by 25.33% and 30.59%, respectively.