A self-consistent algorithm will be proposed to non-parametrically estimate the cause-specific cumulative incidence functions (CIFs) in an interval censored, multiple decrement context. More specifically, the censoring mechanism will be assumed to be a mixture of case 2 interval-censored data with the additional possibility of exact observations. The proposed algorithm is a generalization of the classical univariate algorithms of Efron and Turnbull. However, unlike any previous non-parametric models proposed in the literature to date, the algorithm will explicitly allow for the possibility of any combination of masked modes of failure, where failure is known only to occur due to a subset from the set of all possible causes. A simulation study is also conducted to demonstrate the consistency of the estimators of the CIFs produced by the proposed algorithm, as well as to explore the effect of masking. The paper concludes by applying the method to masked mortality data obtained for Pueblo County, CO, for three risks: death by cancer; cardiovascular failure; or other.