A novel technique for Electroencephalogram (EEG) compression is proposed in this article. This technique models the intrinsic dependency inherent between the different EEG channels. It is based on dipole fitting that is usually used in order to find a solution to the classic problems in EEG analysis: inverse and forward problems. The suggested compression system uses dipole fitting as a first building block to provide an approximation of the recorded signals. Then, (based on a smoothness factor,) appropriate coding techniques are suggested to compress the residuals of the fitting process. Results show that this technique works well for different types of recordings and is even able to provide near- lossless compression for event-related potentials.