Sleep-wake protocols are critical in sensor networks to ensure long-lived operation. However, an open problem is how to develop efficient mechanisms that can be incorporated with sleep-wake protocols to ensure both long-lived operation and a high degree of security. Our contribution in this paper is to address this problem by using local monitoring, a powerful technique for detecting and mitigating control and data attacks in sensor networks. In local monitoring, each node oversees part of the traffic going in and out of its neighbors to determine if the behavior is suspicious, such as, unusually long delay in forwarding a packet. Here, we present a protocol called SLAM to make local monitoring parsimonious in its energy consumption and to integrate it with any extant sleep-wake protocol in the network. The challenge is to enable sleep-wake in a secure manner even in the face of nodes that may be adversarial and not wake up nodes responsible for monitoring its traffic. We prove analytically that the security coverage is not weakened by the protocol. We perform simulations in ns-2 to demonstrate that the performance of local monitoring is practically unchanged while listening energy saving of 30 to 129 times is achieved, depending on the network load.