Analytical modeling of the 802.11e enhanced distributed channel access (EDCA) mechanism is today a fairly mature research area, considering the very large number of papers that have appeared in the literature. However, most work in this area models the EDCA operation through per-slot statistics, namely probability of transmission and collisions referred to ¿slots.¿ In so doing, they still share a methodology originally proposed for the 802.11 Distributed Coordination Function (DCF), although they do extend it by considering differentiated transmission/collision probabilities over different slots. We aim to show that it is possible to devise 802.11e models that do not rely on per-slot statistics. To this purpose, we introduce and describe a novel modeling methodology that does not use per-slot transmission/collision probabilities, but relies on the fixed-point computation of the whole (residual) backoff counter distribution occurring after a generic transmission attempt. The proposed approach achieves high accuracy in describing the channel access operations, not only in terms of throughput and delay performance, but also in terms of low-level performance metrics.