In many survival analysis settings, the assumption of non-informative (i.e. independent) censoring is not valid. Zheng and Klein (1995, 1996) develop a copula-based method for estimating the marginal survival functions of bivariate dependent competing risks data. We expand upon this earlier work and adapt their method to data in which there are three competing risks representing both dependent and independent censoring. Specifically, our extension allows for the estimation of the survival functions of dependent competing risks X and Y in the presence of a third independent competing risk Z. An application to dividend initiation data is presented.