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We present UDDSketch (Uniform DDSketch), a novel sketch for fast and accurate tracking of quantiles in data streams. This sketch is heavily inspired by the recently introduced DDSketch, and is based on a novel bucket collapsing procedure that allows overcoming the intrinsic limits of the corresponding DDSketch procedures. Indeed, the DDSketch bucket collapsing procedure does not allow the derivation of formal guarantees on the accuracy of quantile estimation for data which does not follow a sub-exponential distribution. On the contrary, UDDSketch is designed so that accuracy guarantees can be given over the full range of quantiles and for arbitrary distribution in input. Moreover, our algorithm fully exploits the budgeted memory adaptively in order to guarantee the best possible accuracy over the full range of quantiles. Extensive experimental results on synthetic datasets confirm the validity of our approach.