In this paper, a two-stage coder based near-lossless compression of Electroencephalogram (EEG) is discussed. It consists of wavelet based lossy coding layer (until bitplane n _d ) followed by entropy coding of the wavelet domain residuals. L ^∞ -error bound is fixed in wavelet domain and the corresponding time-domain absolute error variation is studied. Studies show that intermediate demarcating bit-planes (n _d ) register a higher compression and gives a nearly constant time-domain error. Both the normal and epileptic EEG registered a comparable compression performance.