In mobile ad hoc networks (MANETs), broadcasting plays a fundamental role, diffusing a message from a given source node to all the other nodes in the network. Flooding is the simplest and commonly used mechanism for broadcasting in MANETs, where each node retransmits every uniquely received message exactly once. Despite its simplicity, it however generates redundant rebroadcast messages which results in high contention and collision in the network, a phenomenon referred to as broadcast storm problem. Pure probabilistic approaches have been proposed to mitigate this problem inherent with flooding, where mobile nodes rebroadcast a message with a probability p which can be fixed or computed based on the local density. However, these approaches reduce the number of rebroadcasts at the expense of reachability. On the other hand, counter-based approaches inhibit a node from broadcasting a packet based on the number of copies of the broadcast packet received by the node within a random access delay time. These schemes achieve better throughput and reachability, but suffer from relatively longer delay. In this paper, we propose an efficient broadcasting scheme that combines the advantages of pure probabilistic and counter-based schemes to yield a significant performance improvement. Simulation results reveal that the new scheme achieves superior performance in terms of saved-rebroadcast, reachability and latency.