This paper presents a new lightweight algorithm for pruning inactive entries in version vectors (VVs). This algorithm lets each node remove inactive VV entries without any coordination with other nodes. It achieves this feature by devising a new way to compare two version vectors based on loosely synchronized clocks and placing a timing restriction on the behavior of the application. VVs computed by our algorithm can accurately and completely capture the "happened-before" relation between events just like ordinary VVs. This paper proves the correctness of our algorithm as well. 8 Pages