Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. While several different semantics have been proposed, and some have been more successful than others, the exact relationships between the approaches have not yet been fully understood. In this paper, we give new characterizations, using level mappings, of the Fitting semantics, the well-founded semantics, and the weakly perfect model semantics. The results will unmask the well-founded semantics as a stratified version of the Fitting semantics.