For provisioning large-scale online applications such as web search, social networks and advertisement systems, data centers face extreme challenges in providing low latency for short flows (that result from end-user actions) and high throughput for background flows (that are needed to maintain data consistency and structure across massively distributed systems). We propose L2DCT, a practical data center transport protocol that targets a reduction in flow completion times for short flows by approximating the Least Attained Service (LAS) scheduling discipline, without requiring any changes in application software or router hardware, and without adversely affecting the long flows. L2DCT can co-exist with TCP and works by adapting flow rates to the extent of network congestion inferred via Explicit Congestion Notification (ECN) marking, a feature widely supported by the installed router base. Though L2DCT is deadline unaware, our results indicate that, for typical data center traffic patterns and deadlines and over a wide range of traffic load, its deadline miss rate is consistently smaller compared to existing deadline-driven data center transport protocols. L2DCT reduces the mean flow completion time by up to 50% over DCTCP and by up to 95% over TCP. In addition, it reduces the completion for 99th percentile flows by 37% over DCTCP. We present the design and analysis of L2DCT, evaluate its performance, and discuss an implementation built upon standard Linux protocol stack.