Providing safety applications is one of the principal motivations behind deploying vehicular ad hoc networks (VANETs). These applications require fair (i.e., all vehicles get equal fraction of time allocation for their transmissions) and reliable (i.e., transmissions are received with high probably by the intended receivers) broadcasting of relevant driving data. In this paper we compare the performance of IEEE 802.11p and a recent time-division based medium access control protocol, Dynamic Channel Reservation (DCR) in realistic high-density traffic scenarios. We focus on the communication requirements that allow vehicles to receive safety messages well enough in advance to warn the driver in a timely manner and avoid crashes. We observe performance degradation in both schemes as we examine them in congested environments. In such scenarios, in 802.11p, broadcast reliability decreases, while in DCR, some vehicles face starvation, thus the fairness requirement is not met. In order to avoid this situation, we propose a modified version of DCR, fDCR, in which time channels can be occupied by several vehicles, thus fostering a fair channel reservation scheme. Our channel reservation scheme is designed in a way that minimizes packet collisions due to a transmission, in receivers which are close to that transmitter. Furthermore, to enhance the probability of reception in nearby vehicles, which is one of the main communication requirements of safety applications, we propose a low-overhead transmission power control scheme. Our fully distributed power control scheme leverages on the extra transmitted information by DCR to estimate the number of vehicles in its transmission range, and accordingly adjust the transmission power. Experimental results show significant performance gains in cases of both cross-through and non-cross-through traffic for our proposed scheme in comparison with 802.11p and DCR.