Let E be a Fell bundle over an r-discrete principal groupoid Gamma that is
measurewise amenable with respect to every quasi-invariant measure on Gamma
((0)). Let C*(E) be the corresponding C*-algebra and let C-0(E-0) be the di
agonal subalgebra. The Spectral Theorem on Bimodules proved in this pager g
ives a description of C-0(E-0)-bimodules in C*(E).