Several programming constructs have recently been proposed with the purpose of enabling the programmer to encode declassifying information flows within a program that complies with information flow security policies. These constructs may or may not incorporate some means for controlling when, where, what, or by whom the declassification can be set up. In the context of global computing, other forms of controlling declassification that transcend the power of a single declassification construct may turn out to be desirable. In this paper we point out potential unwanted behaviors that can arise in a context where programs that contain declassifying instructions can migrate to computation domains with different security policies. We propose programming language design techniques for tackling such unwanted behaviors and prove soundness of those techniques at the global computation level.