Future safety-related vehicular applications require reliable information exchange provided by cooperative Vehicular Ad-hoc NETworks (VANETs). Although the vehicular WLAN standard IEEE 802.11p has been adapted to the challenging vehicular environment, it has not been adapted to the stringent communication requirements imposed by vehicular applications. In particular, broadcast transmissions are mostly periodic and initiated at common TX powers. This makes potential interferences recurring instead of spurious and lowers the performance of medium access for vehicular applications.In this paper, we propose to leverage recurring interferences by randomly selecting each TX power following a given probability distribution. Such randomization reduces the chances of recurring interferences, and the probability distribution provides control to the applications regarding the required Awareness Quality, in particular by providing a higher Awareness Quality at close range. This concept also reduces congestions by transmitting less at high distances. It is transparent to the applications, and manages to improve the Awareness Quality in a dense highway by a factor 2 to 20, yet at a factor 2 to 3 lower channel load.