As advanced traveler information systems become increasingly prevalent the importance of accurately estimating link travel times grows. Unfortunately, the predominant source of highway traffic information comes from single-trap loop detectors which do not directly measure vehicle speed. The conventional method of estimating speed, and hence travel time, from the single-trap data is to make a common vehicle length assumption and to use a resulting identity relating density, flow, and speed. Hall and Persaud (1989) and Pushkar, Hall, and Acha-Daza (1994) show that these speed estimates are flawed. In this paper we present a methodology to estimate link travel times directly from the single-trap loop detector flow and occupancy data without heavy reliance on the flawed speed calculations. Our methods arise naturally from an intuitive stochastic model of traffic flow. We demonstrate by example on data collected on I-880 that when the loop detector data has a fine resolution (about one second), the single-trap estimates of travel time can accurately track the true travel time through many degrees of congestion. Probe vehicle data and double-trap travel time estimates corroborate the accuracy of our methods in our examples.