The ability of the IEEE 802.11 Medium Access Control (MAC) protocol to perform well in multi-hop ad hoc networks has been recently questioned. We observe levels of spatial reuse that are 30% to 50% away from the theoretical limit. The goal of this paper is to answer the following question: what prevents the IEEE 802.11 MAC protocol from operating at the limit determined by its physical layer? We identify three problems in the contention resolution mechanism of the IEEE 802.11 MAC protocol, and we show that they account for most of the gap separating the actual and optimal performances of the protocol. For each of the problems, we propose a solution that, once implemented, allows us to quantify the impact of the problem on the performance of the IEEE 802.11 MAC protocol. The resulting protocol operates 10% to 15% away from the theoretical limit. Finally, we show that reducing the overhead of the protocol to some negligible quantity brings the spatial reuse of the protocol to the theoretical limits. It also makes apparent the powerful organizing capacity of the IEEE 802.11 MAC protocol.