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A major concern in wireless sensor networks (WSNs) is energy conservation, since battery-powered sensor nodes are expected to operate autonomously for a long time, e.g., for months or even years. Another critical aspect of WSNs is reliability, which is highly application-dependent. In most cases it is possible to trade-off energy consumption and reliability in order to prolong the network lifetime, while satisfying the application requirements. In this paper we propose an adaptive and cross-layer framework for reliable and energy-efficient data collection in WSNs based on the IEEE 802.15.4/ZigBee standards. The framework involves an energy-aware adaptation module that captures the application's reliability requirements, and autonomously configures the MAC layer based on the network topology and the traffic conditions in order to minimize the power consumption. Specifically, we propose a low-complexity distributed algorithm, called ADaptive Access Parameters Tuning (ADAPT), that can effectively meet the application-specific reliability under a wide range of operating conditions, for both single-hop and multi-hop networking scenarios. Our solution can be integrated into WSNs based on IEEE 802.15.4/ZigBee without requiring any modification to the standards. Simulation results show that ADAPT is very energy-efficient, with near-optimal performance.