Due to environmental concerns and strict constraints on interference imposed on other networks, the radiated power of emerging pervasive wireless networks needs to be strictly limited, yet without sacrificing acceptable data rates. Pulsed Time-Hopping Ultra-Wideband (TH-UWB) is a radio technology that has the potential to satisfy this requirement. Although TH-UWB is a multi-user radio technology, non-zero cross-correlation between time-hopping sequences, time-asynchronicity between sources and a multipath channel environment make it sensitive to strong interferers and near-far scenarios. While most protocols manage interference and multiple-access through power control or mutual exclusion, we base our design on rate control, a relatively unexplored dimension for multiple-access and interference management. We further take advantage of the nature of pulsed TH-UWB to propose an interference mitigation scheme that alleviates the need for an exclusion scheme. A source is always allowed to send and continuously adapts its channel code (hence its rate) to the interference experienced at the destination. In contrast to power control or exclusion, our MAC layer is local to sender and receiver and does not need coordination among neighbors not involved in the transmission. We show by simulation that we achieve a significant increase in network throughput compared to alternative designs.