  The SU(3)-Casson invariant for integral homology 3-spheres as studied by
Boden-Herald possesses a 'spectral flow obstruction' to being an integer valued
invariant which depends only on the non-degenerate (perturbed) moduli space of
flat SU(3)-connections. This obstruction is the non-trivial spectral flow of a
family of twisted signature operators in 3-dimensions. The parallel
U(2)-Seiberg-Witten construction also has an obstruction but from the
non-trivial spectral flow of a family of twisted Dirac operators. By taking the
SU(3)-flat and U(2)-Seiberg-Witten equations simultaneously the obstructions
can be made to cancel and an integer invariant is obtained.
