  The light curves of Cepheids and other variable stars in Field A of IC 1613,
obtained with a CCD and no filter ($Wh$ photometry), have been analyzed. It is
possible to separate first overtone from fundamental mode population I Cepheids
taking into account the pulsation amplitude, the shape of the light curve and
the period. The expected separation is verified in the period--luminosity $PL$
diagram. Light curve Fourier parameters have been compared with those of
Magellanic Clouds and galactic Cepheids, in order to point out the effects of
the very low metallicity of IC 1613 on the light curve shape. Population II
Cepheids of IC 1613 can be discriminated from those of population I in the $PL$
diagram, and, taking into account their color, from other red or blue
variables. Their $PL$ relation is consistent with that observed in globular
clusters, nearby dwarf spheroidal galaxies and LMC. We have shown it is
possible to apply the single-phase method for deriving standard photometry $PL$
relations for population I and II Cepheids; therefore with just one accurate
$BVRI$ observation it is possible to use the population I Cepheids for distance
determinations. Some unusual stars have been identified on the basis of
periods, light curve shapes and colors; they appear to be pulsating stars
laying on the extension of $PL$ relation of known anomalous Cepheids. A firmer
classification of these and other faint stars requires further deeper
multicolor observations.
