  Approximating quantiles and distributions over streaming data has been
studied for roughly two decades now. Recently, Karnin, Lang, and Liberty
proposed the first asymptotically optimal algorithm for doing so. This
manuscript complements their theoretical result by providing a practical
variants of their algorithm with improved constants. For a given sketch size,
our techniques provably reduce the upper bound on the sketch error by a factor
of two. These improvements are verified experimentally. Our modified quantile
sketch improves the latency as well by reducing the worst case update time from
$O(1/\varepsilon)$ down to $O(\log (1/\varepsilon))$. We also suggest two
algorithms for weighted item streams which offer improved asymptotic update
times compared to na\"ive extensions. Finally, we provide a specialized data
structure for these sketches which reduces both their memory footprints and
update times.
