This paper focuses on on-demand wireless sensor networks (WSNs) where a wake-up receiver is installed into each node. In on-demand WSNs, each node sends a wake-up signal including a wake-up ID assigned to a specific destination node in order to remotely activate its main radio interface. This wake-up control helps each node to reduce energy consumed during idle periods, however, the wake-up signal transmitted before every data transmission results in overhead, which degrades communication quality and increases energy consumption at each sender node. In order to reduce the overhead for wake-up control, in this paper, we propose three schemes. First, we propose a scheme called Double Modulation (DM), where each node embeds the sensing data to be transmitted into the payload field of a wake-up signal. The destination interprets the wake-up message differently depending on its wake-up state: if it is in a sleep state, it treats the message as a wake-up signal, otherwise it extracts the sensing data from the detected message. Second, we propose a scheme called Overhearing (OH), where each node observes the frames transmitted by a destination node and suppresses the transmission of wake-up signal when detecting the active state of their destination. Finally, we propose a hybrid scheme that combines OH and DM schemes. Our simulation results show that the proposed schemes can effectively reduce the negative impact of wake-up overhead, and significantly improve data collection rate and energy-efficiency in comparison to on-demand WSN without the proposed schemes.