This work presents a wireless multichannel electroencephalogram (EEG) recording system featuring lossless and near-lossless compression of the digitized EEG signal. Two novel, low-complexity, efficient compression algorithms were developed and tested in a low-power platform. The algorithms were tested on six public EEG databases comparing favorably with the best compression rates reported up to date in the literature. In its lossless mode, the platform is capable of encoding and transmitting 59-channel EEG signals, sampled at 500 Hz and 16 bits per sample, at a current consumption of 337 μA per channel; this comes with a guarantee that the decompressed signal is identical to the sampled one. The near-lossless mode allows for significant energy savings and/or higher throughputs in exchange for a small guaranteed maximum per-sample distortion in the recovered signal. Finally, we address the tradeoff between computation cost and transmission savings by evaluating three alternatives: sending raw data, or encoding with one of two compression algorithms that differ in complexity and compression performance. We observe that the higher the throughput (number of channels and sampling rate) the larger the benefits obtained from compression.