Trajectory data is becoming increasingly available and the size of the trajectories is getting larger. In this paper we study the problem of compressing spatio-temporal trajectories such that the most common queries can still be answered approximately after the compression step has taken place. In the process we develop an O(n logk n)-time implementation of the Douglas-Peucker algorithm in the case when the polygonal path of n vertices given as input is allowed to self-intersect.