A new version of Reiter's Default Logic is developed which has a number of advantages: it is computationally much simpler and has some more intuitive properties, such as cumulativity. Furthermore, it is shown that this Default Logic is a limiting case of a Dempster-Shafer framework, thereby demonstrating a strong connection between two apparently very different approaches to reasoning with uncertainty, and opening up the possibility of mixing default and numerical rules within the same framework.