Delay in a duty-cycled network occurs when the sender waits for its receiver to be awake. Exploiting multiple receivers instead of a single receiver at each hop allows the sender to use the node that wakes up the soonest and so reduce delay. However, current MAC-layer anycast protocols either suffer from high signaling or synchronization overhead and are only appropriate for low duty cycle, low traffic scenarios. In this paper, we propose Any-MAC a generic, low overhead extension that can be applied to any existing asynchronous MAC protocol to enable MAC-layer anycast. The extensive research in duty-cycle protocols provides us many MAC protocols, each appropriate for a particular network and application scenario. Thus, to construct an anycast solution to reduce delay for a specific network scenario, Any-MAC simply needs to extend the appropriate MAC protocol designed for that scenario. By applying anycast to existing protocols, X-MAC and NPM, we show that Any-MAC uses only simple modification to the base protocols and improves the performance significantly. Our evaluations in ns-2 show that with Any-MAC, both protocols can achieve 30% improvements in delay by exploiting the inherent route level redundancy in the network.