The application of directional antennas in wireless ad hoc networks brings numerous benefits, such as increased spatial reuse and mitigated interference. Most MAC protocols with directional antennas are based on the RTS/CTS mechanism which works well in wireless ad hoc networks using omni-directional antennas. However, RTS/CTS frames cannot mitigate the interference completely. Besides, they also contribute a lot to the performance overhead. This paper studies the problem from a new perspective. We have found that the transmission success probability under directional transmission and directional reception is quite high when the antenna beamwidth is quite narrow. Motivated by the analytical results, we design a lightweight MAC protocol without RTS/CTS frames. The evaluation results demonstrate that this new protocol performs better than MAC protocols based on the RTS/CTS mechanism. The results also show that a collision-tolerant transmission is feasible under the narrow beam configuration.