 Indeed, with reference to this point we recall that, as extensively discussed in the literature (Suppes &amp; Zanotti 1976; van Fraassen 1982; Jarrett 1984; Shimony 1984; see also the entry on  Bell’s Theorem),  Bell’s locality assumption is equivalent to the conjunction of two other assumptions, viz., in Shimony’s terminology, parameter independence and outcome independence. In view of the experimental violation of Bell’s inequality, one has to give up either one or both these assumptions. The above splitting of the locality requirement into two logically independent conditions is particularly useful in discussing the different status of CSL and deterministic hidden variable theories with respect to relativistic requirements. Actually, as proved by Jarrett himself, when parameter independence is violated, if one had access to the variables which specify completely the state of individual physical systems, one could send faster-than-light signals from one wing of the apparatus to the other. Moreover, in Ghirardi and Grassi (1996) it has been proved that it is impossible to build a genuinely relativistically invariant theory which, in its nonrelativistic limit, exhibits parameter dependence. Here we use the term genuinely invariant to denote a theory for which there is no (hidden) preferred reference frame. On the other hand, if locality is violated only by the occurrence of outcome dependence then faster-than-light signaling cannot be achieved (Eberhard 1978; Ghirardi, Rimini, &amp; Weber 1980). Few years after the just mentioned proof by Bell, it has been shown in complete generality (Ghirardi, Grassi, Butterfield, &amp; Fleming 1993) that the GRW and CSL theories, just as standard quantum mechanics, exhibit only outcome dependence. This is to some extent encouraging and shows that there are no reasons of principle making unviable the project of building a relativistically invariant DRM.