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 ~ 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 (observers frame), reaching ~ 100 keV for one object. The BeppoSAX band in one of our sources, RGB J1629+4008, is dominated by synchrotron emission peaking at ~ 2 x 10^16 Hz, as also shown by its steep (energy index alpha_x ~ 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 ~ 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 ~ 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.
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