Wireless Sensor Networks are complex systems consisting of a number of relatively simple autonomous sensing devices spread on a geographical area. The peculiarity of these devices lies on the constraints they face in relation to their energy reserves and their computational, storage and communication capabilities. The utility of these sensors is to measure certain environmental conditions and to detect critical events in relation to these measurements. Those events thereupon have to be reported to a specific central station namely the “sink”. This data propagation generally has the form of a hop-by-hop transmission. In this framework we work on distributed data propagation protocols which are taking into account the energy reserves of the sensors. In particular following the work of Chatzigiannakis et al. on the Probabilistic Forwarding Protocol (PFR) we present the distributed probabilistic protocol EFPFR, which favors transmission from the less depleted sensors in addition to favor transmissions close to the “optimal line”. This protocol is simple and relies only on local information for propagation decisions. Its main goal is to limit the total amount of energy dissipated per event and therefore to extend the network’s operation duration.