Broadcast is widely used in many wireless ad hoc network operations including servicing source paging and route discovery. However, uncontrolled broadcasting, such as blind flooding, may lead to serious redundant rebroadcasts, contentions and collisions, known as "broadcast storm" problems. Although this problem has been extensively addressed, most studies fail to successfully balance reachability and rebroadcast saving in networks with different node densities. This study proposes an efficient scheme, called DISCOUNT, which combines both DIStance-based and COUNTter-based schemes. DISCOUNT has good reachability and rebroadcast saving, and also provides a good performance under a high-mobility environment. Moreover, DISCOUNT is simple to implement and fully distributed, with no extra control overheads or complex calculations. The simulation results demonstrate that the proposed scheme works well in both sparse and dense networks compared with simple distance-based and counter-based algorithms. Furthermore, since DISCOUNT can keep good balance between reachability and rebroadcast efficiency in various network densities, the dynamic adjusting of counter threshold according to network densities is not necessary. We believe that this property is important in real world implementation.