A repetition in a string x is a substring of x , maximum e ≥ 2, where u is not itself a repetition in w . A run in x is a substring of “maximal periodicity”, where is a repetition and u * a maximum-length possibly empty proper prefix of u . A run may encode as many as repetitions. The maximum number of repetitions in any string is well known to be Θ(nlogn). In 2000 Kolpakov & Kucherov showed that the maximum number of runs in x is O(n); they also described a Θ(n)-time algorithm, based on Farach’s Θ(n)-time suffix tree construction algorithm (STCA), Θ(n)-time Lempel-Ziv factorization, and Main’s Θ(n)-time leftmost runs algorithm, to compute all the runs in x . Recently Abouelhoda et al. proposed a Θ(n)-time Lempel-Ziv factorization algorithm based on an “enhanced” suffix array — a suffix array together with other supporting data structures. In this paper we introduce a collection of fast space-efficient algorithms for computing all the runs in a string that appear in many circumstances to be superior to those previously proposed.