  We examine the role of instrumental systematics in the search for small
amplitude signal components in the presence of large amplitude signals. Current
analyses of variable stars dealing with the above situation seem to ignore the
effects of systematics, albeit the consideration of systematics is quite
routine in the field of extrasolar planets. We show that simultaneous filtering
of the large amplitude component and the systematics leads to residuals with
much better potentials to detect any hidden small amplitude components. The
method is illustrated by selected examples from the Kepler database.
