We present improved algorithms for short cycle decomposition of a graph -a decomposition of an undirected, unweighted graph into edge-disjoint cycles, plus a small number of additional edges. Short cycle decompositions were introduced in the recent work of Chu et al. (FOCS 2018), and were used to make progress on several questions in graph sparsification.For all constants δ ∈ (0, 1], we give an O(mn δ ) time algorithm that, given a graph G, partitions its edges into cycles of length O(log n) 1 δ , with O(n) extra edges not in any cycle. This gives the first subquadratic, in fact almost linear time, algorithm achieving polylogarithmic cycle lengths. We also give an m · exp(O( √ log n)) time algorithm that partitions the edges of a graph into cycles of length exp(O( √ log n log log n)), with O(n) extra edges not in any cycle. This improves on the short cycle decomposition algorithms given by Chu et al. in terms of all parameters, and is significantly simpler.As a result, we obtain faster algorithms and improved guarantees for several problems in graph sparsification -construction of resistance sparsifiers, graphical spectral sketches, degree preserving sparsifiers, and approximating the effective resistances of all edges. * Stanford University. yangpatil@gmail.com. Research supported by the U.S. Department of Defense via an NDSEG fellowship. † University of Toronto. sachdeva@cs.toronto.edu. Research supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC), and a Connaught New Researcher award. ‡ University of Waterloo. z248yu@uwaterloo.ca. This work was done when this author was an undergrad student at the University of Toronto.Combining Theorem 1.2 with [CGP + 18, Theorem 6.1] gives an improved construction of graphical spectral sketches and resistance sparsifiers.