We introduce assured safety arguments, a new structure for arguing safety in which the safety argument is accompanied by a confidence argument that documents the confidence in the structure and bases of the safety argument. This structure separates the major components that have traditionally has been confused within a single safety argument structure. Separation gives both arguments greater clarity of purpose, and helps avoid the introduction of superfluous arguments and evidence. In this paper we describe a systematic approach to establishing both arguments, illustrated with a running example.