This article describes a method for compressing position and identification data for files containing comprehensive trajectory records of all vehicles traversing the same roadway segment over an arbitrary time period, in such a way that no loss of information content occurs. Such complete trajectory records are important for the study of traffic flow theory and could become increasingly relevant as test data against which to study the behavior of autonomous vehicles in a mixed traffic environment. Compression steps include differential encoding, motion prediction, and parsimonious binary storage, plus steps that are unique to the context of vehicle trajectories, including vehicle ID numbers and lane occupancy. The effectiveness of the compression is due, in part, to the strong correlations between positions (and speeds) of vehicles traveling near each other, as well as recognition that certain trajectory artifacts change with spatial and temporal frequencies much lower than the sampling rates. The algorithm is demonstrated on two sets of publicly available complete trajectory records, and compression performance statistics are given. Compression ratios in the range 10:1 to more than 20:1 are achieved for the sample files.