  The presence of muons in air-showers initiated by cosmic ray protons and
nuclei is well established as a powerful tool to separate such showers from
those initiated by gamma-rays. However, so far this approach has been fully
exploited only for ground level particle detecting arrays. In this
contribution, we explore the feasibility of using Cherenkov light from muons as
a background rejection tool for imaging atmospheric Cherenkov telescope arrays
at the highest energies. We adopt an analytical model of the Cherenkov light
from individual muons to allow rapid simulation of a large number of showers in
a hybrid mode. This allows exploration of the very high background rejection
power regime at acceptable cost in terms of computing time. We find that for
very large telescopes ($\gtrsim$20 m diameter), efficient identification of
muons would provide a major improvement with respect to standard background
rejection techniques at energies above several tens of TeVs.
