The initial TCP slow start phase seeks to ramp up data transmission rates quickly to meet available capacity but also to exit the slow start phase before causing undue congestion. Unfortunately, the typical default TCP implementation often exits slow start too early, before capacity has been reached, causing underutilization, particularly detrimental to networks with large capacities and high delays. This study introduces a novel enhancement to TCP slow start - Slow start Exit At Right CHokepoint (SEARCH) - where the link capacity is inferred at the server based on bytes delivered compared to the expected bytes delivered, smoothed to account for link latency variation and normalized to accommodate link capacities. Empirical evaluation over geosynchronous satellite links, low-orbit satellite links, and 4G LTE links shows our approach is a substantial improvement over default TCP implementations by not exiting slow start too early, but better than traditional TCP, too, by exiting slow start before encountering packet loss.