In wireless sensor networks, energy efficiency is crucial to achieving satisfactory network lifetime. To reduce the energy consumption significantly, a node should turn off its radio most of the time, except when it has to participate in data forwarding. We propose a new technique, called sparse topology and energy management (STEM), which efficiently wakes up nodes from a deep sleep state without the need for an ultra low-power radio. The designer can trade the energy efficiency of this sleep state for the latency associated with waking up the node. In addition, we integrate STEM with approaches that also leverage excess network density. We show that our hybrid wakeup scheme results in energy savings of over two orders of magnitude compared to sensor networks without topology management. Furthermore, the network designer is offered full flexibility in exploiting the energy-latency-density design space by selecting the appropriate parameter settings of our protocol.