Non-Interference is an information flow security property which aims to protect confidential data by ensuring the complete absence of any information flow from high level entities to low level ones. However, this requirement is too demanding when dealing with real applications: indeed, no real policy ever guarantees a total absence of information flow. In order to deal with real applications, it is often necessary to allow mechanisms for downgrading or declassifying information such as information filters and channel control. In this paper we introduce the notion of Delimited Persistent Stochastic Non-Interference (D_PSNI) that allows information to flow from a higher to a lower security level through a downgrader. We provide two algebraic characterizations of D_PSNI and prove some compositionality properties. Finally, we present a decision algorithm and discuss its time complexity.