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This paper bears on the design and the quantitative evaluation of MAC mechanisms for wireless ad-hoc networks with performance guarantees. By this, we mean mechanisms where each accepted connection obtains a minimum rate or equivalently a minimum SINR level - which is not guaranteed by CSMA/CA - and which are adapted to the wireless ad-hoc network framework, namely are decentralized, power efficient and provide a good spatial reuse. Two such access control algorithms are defined and compared. Both take the interference level into account to decide on the set of connections which can access the shared channel at any given time. The main difference between the two is the possibility or not of adjusting the transmission power of the nodes. A thorough comparison of the performance of these two mechanisms and CSMA/CA is presented, based on a mix of analytical models and simulation and on a comprehensive set of performance metrics which include spatial reuse and power efficiency. Different network topologies, propagation environments and traffic scenarios are considered. The main aim of our study is to identify which of the proposed mechanisms outperforms CSMA/CA best depending on the scenario.