Many of the inferences we draw in our day-to-day reasoning are defeasible—their conclusions can be withdrawn in the light of new evidence. This inferential property, known as non-monotonicity, requires the development of non-standard logics to model our reasoning practices, for, in standard logic, the conclusions drawn from a premise set are never withdrawn when new premises are added to that set. Non-standard logics, however, face a unique challenge. Defeasible inferences have varying strengths and how to model the interaction between such inferences is an outstanding question. In this paper, I provide an answer to this question within the framework of the default logic originally proposed by Reiter (1980) and recently developed by Horty (2012). Focusing on a few sample cases, I show where Horty (2012)’s answer to the above question stands in need of development and how my proposed revisions to his account address these deficiencies. I also consider other developments of Reiter (1980)’s default logic which avoid some of Horty (2012)’s problems and suggest that these accounts face a fundamental difficulty which my account does not.