Data compression techniques have been widely used to process and transmit huge amount of EEG data in real-time and remote EEG signal processing systems. In this paper we propose a lossy compression technique, F-shift, to compress EEG signals for remote depth of Anaesthesia (DoA) monitoring. Compared with traditional wavelet compression techniques, our method not only preserves valuable clinical information with high compression ratios, but also reduces high frequency noises in EEG signals. Moreover, our method has negligible compression overheads (less than 0.1 seconds), which can greatly benefit real-time EEG signal monitoring systems. Our extensive experiments demonstrate the efficiency and effectiveness of the proposed compression method.