Existing literature has argued that all-cause mortality projections based on cause specific mortality experience have a number of serious drawbacks. There is a widely shared consensus that projections of all-cause mortality based on cause-specific mortality generally perform worse than the direct projection of all-cause mortality because if (1) the inferior cause of death mortality data and (2) the complex dependence structure between causes of death. In this paper, we use the recent WHO access version causes of death data to address this issue in a multi-population context. We propose a two-stage beta-convergence test to capture the cause-specific mortality dynamics between different countries and between different causes, summarizing the observed causes of death dependence structure. We incorporate international coherence and inter-cause coherence suggested by the two-stage beta-convergence test in a new nestedCoDLi-Lee model. We show that the all-cause mortality projections produced by the nestedCoDLi-Lee model, perform more or less equally well in sample as the ones from the Lee-Carter model and the ones from the Li-Lee model. However, in contrast to results from earlier studies, we find that the all-cause mortality projections of nestedCoDLi-Lee have a better out-of-sample performance in a long forecast horizon. Moreover, for the case of the Netherlands, about 2 years higher remaining life expectancy projections of 67-year-old Dutch males is obtained by the nestedCoDLi-Lee model.