Recent research shows the potential of variable-range transmission power control on the physical network connectivity, the network capacity, and the energy savings in wireless multi-hop networks. In this dissertation, power control in medium access control is exploited, a fundamental problem in all networks whose basis is a broadcast channel. Traditional contention-based MAC protocols resolve collisions by backing off in time. In contrast, a transmitter that backs off in space is considered; it reduces its transmission power. This is analogous to increasing the size of the contention window in temporal backoff. This approach is called to backing off in space power backoff (PB) and is incorporated into a carrier sense multiple access (CSMA) protocol as CSMA/PB. While the throughput per unit energy of CSMA/PB exceeds that of the IEEE 802.11 protocol, often quite substantially, the use of power control introduces unfairness. A new hidden-terminal problem that arises from the link asymmetries associated with the use of transmission power control is identified and an analytical model relating throughput to the transmission power level and backoff window size is developed. Using the model, a backoff algorithm that adjusts the dimensions of both time and space (TS) is proposed. The idea in CSMA/TS is that the opportunity for nodes using low transmission power is higher than for nodes using high transmission power. CSMA/TS achieves a high fairness index values while preserving total throughput and throughput per unit of energy. The feedback mechanism used in current contention-based protocols is very limited and fails to distinguish reasons for transmission failure. A new cooperative feedback mechanism is proposed in which nodes that overhear some or all of the transmission provide feedback to the sender, allowing the sender to distinguish between a collision at the receiver and a receiver that has moved out of range, and respond to each outcome differently. Cooperative feedback allows a node to decide when to increase or to decrease its transmission power, enabling an efficient search of the power space for the appropriate transmission power. The resulting protocol using variable power backoff (VPB), CSMA/VPB further improves throughput per unit energy and extends network lifetime.