In this paper we compare two information flow security properties: the lazy security (L-Sec) [11] and the Bisimulation Non-deducibility on Compositions (BNDC) [4]. To make this we define the Failure Non-deducibility on Compositions, a failure semantics version of the BNDC. The common specification language used for the comparison is the Security Process Algebra [4], an extension of CCS [8] which permits to describe systems where actions belong to two different levels of confidentiality. We prove that BNDC applied to a restricted class ofsystems,the low-deterministic and non-divergent ones, is equal to L-Sec. So these two properties, which are based on quite different underlying intuitions, become the same if we add some conditions to BNDC.