In previously published work (Zhu and Kivelson, 1991) the spatial distribution of compressional magnetic pulsations of period 2--20 min in the outer magnetosphere was described. In this companion paper, we study some specific compressional events within our data set, seeking to determine the structure of the waves and identifying the wave generation mechanism. We use both the magnetic field and three-dimensional plasma data observed by the ISEE 1 and/or 2 spacecraft to characterize eight compressional ULF wave events with frequencies below 8 mHz in the outer magnetosphere. High time resolution plasma data for the event of July 24, 1978, made possible a detailed analysis of the waves. Wave properties specific to the event of July 24, 1978, can be summarized as follows: (1) Partial plasma pressures in the different energy ranges responded to magnetic field pressure differently. In the low-energy range they oscillated in phase with the magnetic pressure, while oscillations in higher-energy ranges were out-of-phase. (2) Perpendicular wavelengths for the event were determined to be 60,000 and 30,000 km in the radial and azimuthal directions, respectively. Wave properties common to all events can be summarized as follows: (1) Compressional Pc 5 wave activity is correlated with &bgr;, the ratio of the plasma pressure to the magnetic pressure; the absolute magnitude of the plasma pressure plays a minor role for the wave activity. (2) The magnetic equator is a node of the compressional perturbation of the magnetic field. (3) The criterion for the mirror mode instability is often satisfied near the equator in the outer magnetosphere when the compressional waves are present. We believe these waves are generated by internal MHD instabilities. ¿ American Geophysical Union 1994