  Extreme-mass-ratio inspirals will be prized sources for the upcoming
space-based gravitational-wave observatory LISA. The hunt for these is beset by
many open theoretical and computational problems in both source modeling and
data analysis. We draw attention here to one of the most poorly understood: the
phenomenon of non-local correlations in the space of
extreme-mass-ratio-inspiral signals. Such correlations are ubiquitous in the
continuum of possible signals (degeneracy), and severely hinder the search for
actual signals in LISA data. However, they are unlikely to manifest in a
realistic set of putative signals (confusion). We develop an inventory of new
analysis tools in order to conduct an extensive qualitative study of degeneracy
- its nature, causes, and implications. Previously proposed search strategies
for extreme-mass-ratio inspirals are reviewed in the light of our results, and
additional guidelines are suggested for the scientific analysis of such
sources.
