For a general C*-correspondence E a canonical saturated invariant ideal, on which the correspondence is not supported, is identified. The quotient correspondence is formed and the Cuntz-Pimsner C*-algebra of it is identified both as a relative Cuntz-Pimsner algebra for E, and as a quotient of the Cuntz-Pimsner algebra for E . For the C*-correspondence arising from a topological quiver this process amounts to restricting the base space of vertices to the closed subspace supporting the space of edges.

The author acknowledges support, in connection with this research, from the Natural Sciences and Engineering Research Council of Canada.