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Data storage and data communication currently pose a major problem for all parties involved with power quality and power systems monitoring. The problem arises from the tremendous amount of data involved. There is a common desire in the power industry to find new techniques for high-accuracy data compression and data storage. This paper introduces the details of a novel data-compression technique that is very suitable for application to power-quality waveforms, in particular, and to power system disturbance waveforms in general. The new technique is developed using adaptive neuro-fuzzy techniques. The paper explains the mechanics of the new technique. Full technique implementation details are given, and test cases based on power-quality waveforms are analyzed.