****************************************************** PR # 32233 The compactness of radio-selected BL Lac objects and their detection in gamma-rays indicate that Compton scattering plays a fundamental role in the physics of these objects. We propose to observe the three X-ray-brightest BL Lacs from a complete radio-selected PSPC/IPC-observed sample that show evidence of a flat tail above 1-2 keV, possibly associated with an emerging Compton component. Characterizing the hard Compton tails will allow us to (1) determine the physical parameters in these sources, (2) distinguish among possible origins for the seed photons, and (3) contrast the high energy properties of radio-selected BL Lacs, poorly studied above 2~keV, with the distinct but related class of X-ray-selected BL Lacs, which are well studied and app ******************************************************