  According to Bell's theorem a large class of hidden-variable models obeying
Bell's notion of local causality conflict with the predictions of quantum
mechanics. Recently, a Bell-type theorem has been proven using a weaker notion
of local causality, yet assuming the existence of perfectly correlated event
types. Here we present a similar Bell-type theorem without this latter
assumption. The derived inequality differs from the Clauser-Horne inequality by
some small correction terms, which render it less constraining.
