We present new BeppoSAX LECS , MECS , and PDS observations of four flat–spectrum radio quasars ( FSRQ ) having effective spectral indices \alpha _ { ro } and \alpha _ { ox } typical of high-energy peaked BL Lacs . Our sources have X–ray–to–radio flux ratios on average \sim 70 times larger than “ classical ” FSRQ and lie at the extreme end of the FSRQ X–ray–to–radio flux ratio distribution . The collected data cover the energy range 0.1 - 10 keV ( observer ’ s frame ) , reaching \sim 100 keV for one object . The BeppoSAX band in one of our sources , RGB J1629+4008 , is dominated by synchrotron emission peaking at \sim 2 \times 10 ^ { 16 } Hz , as also shown by its steep ( energy index \alpha _ { x } \sim 1.5 ) spectrum . This makes this object the first known FSRQ whose X–ray emission is not due to inverse Compton radiation . Two other sources display a flat BeppoSAX spectrum ( \alpha _ { x } \sim 0.7 ) , with weak indications of steepening at low X–ray energies . The combination of BeppoSAX and ROSAT observations , ( non-simultaneous ) multifrequency data , and a synchrotron inverse Compton model suggest synchrotron peak frequencies \approx 10 ^ { 15 } Hz , although a better coverage of their spectral energy distributions is needed to provide firmer values . If confirmed , these values would be typical of “ intermediate ” BL Lacs for which the synchrotron and inverse Compton components overlap in the BeppoSAX band . Our sources , although firmly in the radio–loud regime , have powers more typical of high–energy peaked BL Lacs than of FSRQ , and indeed their radio powers put them near the low–luminosity end of the FSRQ luminosity function . We discuss this in terms of an anti-correlation between synchrotron peak frequency and total power , based on physical arguments , and also as possibly due to a selection effect .