In this paper, a novel transmit power control protocol for vehicular ad-hoc networks (VANETs) is proposed that aims to improve the reliability of safety-critical broadcasts while also maximizing the transmission range. Large transmission ranges are often desirable in order to ensure that safety-critical messages reach as many vehicles as possible, particularly in highvelocity situations. However, larger transmit powers also lead to increased channel contention and packet collisions. Further, vehicles in close proximity of the sender are likely to benefit the most from successfully receiving safety-critical information, requiring protocols that maximize the reliability of broadcasts over short distances. As a consequence, this work proposes an adaptive transmit power control approach that balances these two conflicting goals, i.e., maximizing the number of packets that are successfully received by nearby vehicles, while keeping the transmit power as large as possible to reach vehicles at larger distances. This proposed protocol incurs minimum additional overhead (since it is primarily based on simple overhearing) and works well in both highway and urban traffic scenarios.