Broadcast transmissions are the predominate form of network traffic in a VANET. However, since there is no MAC-layer recovery on broadcast frames within an 802.11-based VANET, the reception rates of broadcast messages can become very low, especially under saturated conditions. In this paper, we present an adaptive broadcast protocol that improves the reception rates of broadcast messages. We rely on the observation that a node in a VANET is able to detect network congestion by simply analyzing the sequence numbers of packets it has recently received. Based on the percentage of packets that are successfully received in the last few seconds, a node is able to dynamically adjust the contention window size and thus improve performance.