Along with the success of IEEE 802.11-compliant WLANs, the Distributed Coordinated Function (DCF) specified as the contention-based medium access mechanism in IEEE 802,11 has been widely used to support applications in new regimes. A thorough understanding of the characteristics of IEEE 802.11 DCF is therefore a research focus. DCF assumes the binary exponential backoff algorithm (BEBA), Several existing models that characterize BEBA as a p-persistent scheme have ignored several subtle protocol details. This has practically constrained the models from being applied in a broader range of configurations, e.g., small contention window, and from being further extended, e.g. 802.11e EDCA. In this paper, we develop an analytical model that captures the subtlety, and faithfully describes the channel activities as governed by DCF. Based on the devised model, we perform a rigorous analysis on the saturation throughput performance in a single-hop WLAN. We also identify, by clearly defining and thus being able to differentiate the two terms, attempt probability and transmission probability, an erroneous extension made to Bianchi's model . All the findings are corroborated by ns-2 simulation.