The abundance of wireless devices necessitates efficient contention resolution among competing users. With different approaches and channel reservation techniques in use, the ultimate resolution approach still remains similar to pure ALOHA or slotted ALOHA. It has been proven that no approach could achieve a better throughput than pure ALOHA or slotted ALOHA if users are randomly competing with each other. In this work, we investigate an efficient mechanism to improve contention resolution among competing users in dense wireless networks with periodic traffic. Our approach is to use transmission perturbation among competing users in order to avoid repeated collisions down the road. Analysis and performance evaluations show that our new design, Perturbation-based MAC (perMAC), achieves a high throughput and is rather stable.