Given a graph G and integers k 1 , k 2 , and k 3 , the unit interval editing problem asks whether G can be transformed into a unit interval graph by at most k 1 vertex deletions, k 2 edge deletions, and k 3 edge additions. We give an algorithm solving this problem in time 2 O(k log k) · (n + m), where k := k 1 + k 2 + k 3 , and n, m denote respectively the numbers of vertices and edges of G. Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations.Our algorithm implies the fixed-parameter tractability of the unit interval edge deletion problem, for which we also present a more efficient algorithm running in time O(4 k · (n + m)). Another result is an O(6 k · (n + m))-time algorithm for the unit interval vertex deletion problem, significantly improving the algorithm of van 't Hof and Villanger, which runs in time O(6 k · n 6 ).