The recent deployment of data-rich smart phones has led to a fresh impetus for understanding the performance of wide area ad hoc networks. The most popular medium access mechanism for such ad hoc networks is CSMA/CA with RTS/CTS. In CSMA-like mechanisms, spatial reuse is achieved by implementing energy-based guard zones. We consider the problem of simultaneously scheduling the maximum number of links that can achieve a given signal to interference ratio (SIR). In this paper, using tools from stochastic geometry, we study and maximize the medium access probability of a typical link. Our contributions are two-fold: (i) We show that a simple modification to the RTS/CTS mechanism, viz., changing the receiver yield decision from an energy-level guard zone to an SIR guard zone, leads to performance gains; and (ii) We show that this combined with a simple modification to the transmit power level--setting it inversely proportional to the square root of the link gain--leads to significant improvements in network throughput. Further, this simple power-level choice is no worse than a factor of two away from optimal over the class of all "local" power level selection strategies for fading channels, and further is optimal in the non-fading case. The analysis relies on an extension of the Matérn hard core point process which allows us to quantify both these SIR guard zones and this power control mechanism.