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We present the results of recent $BeppoSAX$ observations of the two BL Lac objects OJ 287 and MS 1458+22 in bright optical states and of simultaneous photometric measurements in the bandpasses from $I$ to $U$. OJ 287 was observed in November 2001 and MS 1458+22 in February of the same year. The X-ray flux of OJ 287 was rather low, $F$(2-10 keV$) = (1.35\pm0.15)\times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$ and its spectrum is well described by a single power law with an energy index $0.45\pm0.08$, flatter than that measured in the optical, equal to $1.53\pm0.03$. The X-ray emission of MS 1458+22 was characterized by a low flux level of $F$(2-10 keV$) = (7.5\pm0.6)\times 10^{-13}$ erg cm$^{-2}$ s$^{-1}$, with a steeper spectral index of $1.71\pm0.15$, while in the optical it was $0.99\pm0.06$. We show that the broad-band SEDs of these two sources can be well represented by log-parabolic spectral laws and evaluate their parameters. This law, already observed for the synchrotron components of other BL Lac sources, can be explained if the emitting particles are accelerated by some statistical mechanism having a probability of energy gain that is a decreasing function of the energy itself.