We report on the Beppo SAX observations of four “ extreme ” BL Lacs , selected to have high synchrotron peak frequencies .
All have been detected also in the PDS band .
For 1ES 0120+340 , PKS 0548–322 and H 2356–309 the spectrum is well fitted by a convex broken power-law , thus locating the synchrotron peak around 1–4 keV .
1ES 1426+428 presents a flat energy spectral index ( \alpha _ { x } = 0.92 ) up to \sim 100 keV , thus constraining the synchrotron peak to lie near or above that value .
For their extreme properties , all sources could be strong TeV emitters .

KEYWORDS : BL Lacertae objects : individual : 1ES 0120+340 , PKS 0548-322 , 1ES 1426+428 , H 2356-309 — X–rays : general — TeV : general