  The recent BeppoSAX observations of the BL Lac objects Mkn 501 and 1ES
2344+514 have shown that the synchrotron spectrum of these objects peaks, in a
v-vF(v) representation, at energies at or above 100 keV. One can wonder if
these are the most extreme examples of hard synchrotron blazars, or if they are
the first cases of a more numerous class of sources. Here I propose the
existence of a class of even more extreme BL Lac objects, whose synchrotron
spectrum peaks at or above 1 MeV. Based on the observational trend found
between the location of the synchrotron peak and the bolometric power of BL Lac
objects, it is argued that the proposed extreme sources could have escaped
detection (in any band) so far, or could have been classified as galaxies, and
their "BL Lac-ness" could be revealed by INTEGRAL.
