  The effective observation time of Imaging Air Cherenkov Telescopes (IACTs)
plays an important role in the detection of gamma-ray sources, especially when
the expected flux is low. This time is strongly limited by the atmospheric
conditions. Significant extinction of Cherenkov light caused by the presence of
clouds reduces the photon detection rate and also complicates or even makes
impossible proper data analysis. However, for clouds with relatively high
atmospheric transmission, high energy showers can still produce enough
Cherenkov photons to allow their detection by IACTs. In this paper, we study
the degradation of the detection capability of an array of small-sized
telescopes for different cloud transmissions. We show the expected changes of
the energy bias, energy and angular resolution and the effective collection
area caused by absorption layers located at 2.5 and 4.5 km above the
observation level. We demonstrate simple correction methods for reconstructed
energy and effective collection area. As a result, the source flux that is
observed during the presence of clouds is determined with a systematic error of
< 20%. Finally, we show that the proposed correction method can be used for
clouds at altitudes higher than 5 km a.s.l.. As a result, the analysis of data
taken under certain cloudy conditions will not require additional
time-consuming Monte Carlo simulations.
