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Organizations that collect and sell data face increasing scrutiny for the discriminatory use of data. We propose a novel unsupervised approach to map data into a compressed binary representation independent of sensitive attributes. We show that in an information bottleneck framework, a parsimonious representation should filter out information related to sensitive attributes if they are provided directly to the decoder. Empirical results show that the method achieves state-of-the-art accuracy-fairness trade-off and that explicit control of the entropy of the representation bit stream allows the user to move smoothly and simultaneously along both rate-distortion and rate-fairness curves.