Recent technological advances in wireless body sensor networks have made it possible for the development of innovative medical applications to improve health care and the quality of life. By using miniaturized wireless electroencephalography (EEG) sensors, it is possible to perform ambulatory EEG recording and real-time healthcare applications. One master consideration in using such battery-powered wireless EEG monitoring system is energy constraint at the sensor side. The traditional EEG streaming approach imposes an excessive power consumption, as it transmits the entire EEG signals wirelessly. Therefore, innovative solutions to alleviate the total power consumption at the receiver are highly desired. This work introduces the use of the discrete wavelet transform and compressive sensing algorithms for scalable EEG data compression in wireless sensors in order to address the power and distortion constraints. Encoding and transmission power models of both systems are presented which enable analysis of power and performance costs. We then present a theoretical analysis of the obtained distortion caused by source encoding and channel errors. Based on this analysis, we develop an optimization scheme that minimizes the total distortion for different channel conditions and encoder settings. Using the developed framework, the encoder can adaptively tune the encoding parameters to match the energy constraint without performance degradation.