The emergence of new criteria specifically adapted to multidatabase systems, in response to constraints imposed by global serializability, leads to restrictive hypotheses in order to ensure correctness of executions. This is the case with the two level serializability presented in [6], that ensures strongly correct executions if transaction programs are Local Database Preserving (LDP). The main drawback of the LDP hypothesis is that it relies on rigorous programming. The principal objective of this paper has been to suppress this drawback while conserving the strong correctness of 2LSR executions We propose defining precisely the notion of value dependencies, and managing them so as not to impose the LDP property.