  Cosmic opacity for very high-energy gamma rays ($E>10$ TeV) due to the
interaction with the extragalactic background light can be strongly reduced
because of possible Lorentz-violating terms in the particle dispersion
relations expected, e.g., in several versions of quantum gravity theories. We
discuss the possibility to use very high energy observations of blazars to
detect anomalies of the cosmic opacity induced by LIV, considering in
particular the possibility to use -- besides the bright and close-by BL Lac Mkn
501 -- extreme BL Lac objects. We derive the modified expression for the
optical depth of $\gamma$ rays considering also the redshift dependence and we
apply it to derive the expected high-energy spectrum above 10 TeV of Mkn 501 in
high and low state and the extreme BL Lac 1ES 0229+200. We find that, besides
the nearby and well studied BL Lac Mkn 501 -- especially in high state --,
suitable targets are extreme BL Lac objects, characterized by quite hard TeV
intrinsic spectra likely extending at the energies relevant to detect LIV
features.
