  We describe a method of adding tails to C*-correspondences which generalizes
the process used in the study of graph C*-algebras. We show how this technique
can be used to extend results for augmented Cuntz-Pimsner algebras to
C*-algebras associated to general C*-correspondences, and as an application we
prove a gauge-invariant uniqueness theorem for these algebras. We also define a
notion of relative graph C*-algebras and show that properties of these
C*-algebras can provide insight and motivation for results about relative
Cuntz-Pimsner algebras.
