  It is shown that a C*-algebra generated by any faithful covariant
representation of a Hilbert bimodule X is canonically isomorphic to the crossed
product associated to X provided that Rieffel's induced representation functor
X-ind is topologically free. It is discussed how this result could be applied
to universal C*-algebras generated by relations with a circle gauge action. In
particular, it leads to generalizations of isomorphism theorems for various
crossed products, and is shown to be equivalent to Cuntz-Krieger uniqueness
theorem for finite graph C*-algebras (on that occasion an intriguing
realization of Cuntz-Krieger algebras as crossed products by Exel's
interactions is discovered).
