Energy-efficient transmission scheme is very essential for Wireless Personal Area Networks (WPNs) for maximizing the lifetime of energy-constrained wireless devices and assuring the required QoS in the actual physical transmission at each allocated TDMA time slot. We therefore propose the minimum energy (ME) criterion based adaptive transmission scheme which determines the optimum combination of transmit power, physical data rate and fragment size required to simultaneously minimize the energy consumption and satisfy the required QoS in each assigned time duration. The improved performances offered by the proposed algorithm are demonstrated via computer simulation in terms of throughput and energy consumption.