Abstract: The Enriques criterion for unirationality of conic bundles states that if X is a conic bundle over P^2, then X is unirational if and only if the conic bundle admits a rational multisection. Furthermore, if X is unirational but not rational, then such a rational multisection necessarily has even degree. In this talk, we report on joint work in progress with Jeffrey Diller and Eric Riedl studying when such a conic bundle X -> P^2 admits a degree 2 rational multisection.