We performed an observational program with the X-ray satellite BeppoSAX to study objects with extreme synchrotron peak frequencies (nu_peak > 1 keV). Of the seven sources observed, four showed peak frequencies in the range 1-5 keV, while one (1ES 1426+428) displayed a flat power law spectrum (alpha= 0.92), locating its synchrotron peak at or above 100 keV. This is the third source of this type ever found, after Mkn 501 and 1ES 2344+514. Our data confirm the large nu_peak variability of this class of sources, compared with lower peaked objects. The high synchrotron peak energies, flagging the presence of high energy electrons, make the extreme BL Lacs also good candidates for TeV emission, and therefore good probes for the IR background.