We introduce hi-trees, a new visual representation for hierarchical data in which, depending on the kind of parent node, the child relationship is represented using either containment or links. We give a drawing convention for hi-trees based on the standard layered drawing convention for rooted trees, then show how to extend standard bottom-up tree layout algorithms to draw hi-trees in this convention. We also explore a number of other more compact layout styles for layout of larger hi-trees and give algorithms for computing these. Finally, we describe two applications of hi-trees: argument mapping and business decision support.