End-to-end latency in interactive systems is detrimental to performance and usability, and comes from a combination of hardware and software delays. While these delays are steadily addressed by hardware and software improvements, it is at a decelerating pace. In parallel, short-term input prediction has shown promising results in recent years, in both research and industry, as an addition to these efforts. We describe a new prediction algorithm for direct touch devices based on (i) a state-of-the-art finite-time derivative estimator, (ii) a smoothing mechanism based on input speed, and (iii) a post-filtering of the prediction in two steps. Using both a pre-existing dataset of touch input as benchmark, and subjective data from a new user study, we show that this new predictor outperforms the predictors currently available in the literature and industry, based on metrics that model user-defined negative side-effects caused by input prediction. In particular, we show that our predictor can predict up to 2 or 3 times further than existing techniques with minimal negative side-effects.