We consider the media-access control problem for nodes with heavy traffic in single-destination wireless networks. We assume that each source transmits in each time slot according to a transmission probability, which is a continuous value between 0 and 1. Our goal is to determine the values of the transmission probabilities so that the network throughput is maximized. In this paper, we show that the maximum throughput is achieved only if these values are either 0 or 1. We obtain closed-form results for optimal throughput for networks that operate under a homogenous situation in which the expected value of the received power at the destination is the same for each source. We then extend our studies to more general networks, which rely on exhaustive search for the optimal set of transmissions. The search has exponential complexity and is feasible only for networks with small or moderate sizes. Thus, we also develop heuristic algorithms, which have polynomial-time complexity and are suitable for large and general networks.