Remote wireless monitoring of physiological signals has emerged as a key enabler for biotelemetry and can significantly improve the delivery of healthcare. Improving the energy-efficiency and battery-lifetime of the monitoring units without sacrificing the acquired signal quality is a key challenge in large-scale deployment of bio-electronic systems for remote wireless monitoring. In this paper, we present a design methodology for low power wireless monitoring of Electroencephalography (EEG) data. The proposed design performs a real-time accuracy energy trade-off by controlling the volume of transmitted data based on the information content in the EEG signal. We consider the effect of different system parameters in order to design an optimal system. Our analysis shows that the proposed system design approach can provide significant savings in transmitter power with minimal impact on the monitored EEG signal accuracy. We analyze the impact of noise of the wireless channel and show that an adaptive compression system has better performance for BER < 10-4.