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, five revealed or confirmed their extreme nature. Four showed peak frequencies in the range 1-5 keV, while one (1ES 1426+428) displayed a flat power law spectrum (alpha_x =0.92+/-0.04) which locates 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. In the context of the whole blazar class, the broad band properties of these objects confirm the scenario of a synchrotron peak smoothly spanning the IR - X-ray range, which explains the multi-frequency properties of the blazar class. Our data also confirm the large nu_peak variability which seems to characterize this class of sources, compared with lower nu_peak objects. Given the high synchrotron peak energies, which flag the presence of high energy electrons, these extreme BL Lacs are also good candidates for TeV emission, and therefore good probes of the IR background.