Rare events detection is one of the main applications in Wireless Sensor Networks (WSN) and is currently a central concern of a vast literature. Compressed Sensing (CS) theory has been proved to be quite adapted to this objective. Although this is not the first work on applying CS to sparse events detection in WSN, it is the first to highly justify the validity of the targets detection and counting problem formulation. In order to enhance the CS recovery capacity in WSN, this work considers an approach based on a coherence reduction of the sensing matrix premised on the transmitted power control (PC). Simulation results prove that, under the constraint of equal power consumption, the detection and counting performance is improved when the proposed power control scheme is employed compared to the case without PC.