This paper considers a relayed broadcast in IEEE 802.11 wireless local area (WLAN) networks. In the relayed broadcast, a source node intends to deliver data frames to many nodes beyond its coverage and all the nodes except the source node attempt to relay the received data frames in a contention-based and distributed manner. This traffic dissemination scheme, referred to as flooding, has several problems. As the number of nodes increases, the contention for channel access becomes intensified, resulting in a severe problem of collision and interference, and at the same time, many duplicate frames are unnecessarily transmitted. In order to mitigate contention and redundancy in the relayed broadcast, this paper proposes a bimodal flooding scheme combining two approaches. The first approach aims to relieve contention by deferring the transmission of data frames based on the number of neighbor nodes. Meanwhile, to suppress redundant transmission of data frames, the second approach introduces a novel index of duplication ratio, with which data frames are discarded probabilistically. In this way, the former contributes to the reliable transmission of broadcasting traffic and the latter is effective to decrease its dissemination time. Via simulation study, the performance of several flooding schemes are compared and analyzed in diverse aspects.