Growing Internet usage on mobile devices in cellular networks makes it increasingly important to assure good performance for web traffic, which often consists of many short-lived TCP flows. For TCP, and in the future likely also for QUIC, CUBIC is the most widely deployed congestion control algorithm. With Linux, HyStart is used as default Slow Start algorithm. In this paper we investigate performance impairments occurring when the combination of CUBIC and HyStart is used in low-delay cellular networks. To explain the problem in detail, we present measurements of characteristic per-packet round-trip times caused by uplink scheduling in mobile networks. Inherent round-trip time variations often trigger an early exit of Slow Start, causing CUBIC to underutilize the available capacity. In addition, we extend earlier throughput models for TCP CUBIC to accurately estimate the throughput for short-lived flows as a function of the congestion window size at the Slow Start exit point. We validate the model by measurement results. Further, we propose two HyStart improvements enhancing TCP CUBIC’s performance significantly. In our LTE testbed the mean throughput of a 5MB data transfer increases by 10.5%. Given the nature of web traffic, these fixes can improve the web experience of users noticeably. This shows the importance of measurements, testing, and subsequent optimizations when designing and evaluating transport and congestion control mechanisms for mobile networks.