  The spin modulated gravitational wave signals, which we shall call smirches,
emitted by stellar mass black holes tumbling and inspiralling into massive
black holes have extremely complicated shapes. Tracking these signals with the
aid of pattern matching techniques, such as Wiener filtering, is likely to be
computationally an impossible exercise. In this article we propose using a
mixture of optimal and non-optimal methods to create a search hierarchy to ease
the computational burden. Furthermore, by employing the method of principal
components (also known as singular value decomposition) we explicitly
demonstrate that the effective dimensionality of the search parameter space of
smirches is likely to be just three or four, much smaller than what has
hitherto been thought to be about nine or ten. This result, based on a limited
study of the parameter space, should be confirmed by a more exhaustive study
over the parameter space as well as Monte-Carlo simulations to test the
predictions made in this paper.
