Abstract: Representing a triangulated two manifold using a single triangle strip is an NP-complete problem. By introducing a few Steiner vertices, recent works find such a single-strip, and hence a linear ordering of edge-connected triangles of the entire triangulation. In this paper, we extend previous results [10] that exploit this linear ordering in efficient triangle-strip management for high-performance rendering. We present new algorithms to generate single-strip representations that follow different user defined constraints or preferences in the form of edge weights. These functional constraints are application dependent. For example, normal-based constraints can be used for efficient rendering after visibility culling, or spatial constraints for highly coherent vertex-caching. We highlight the flexibility of this approach by generating single-strips with preferences as arbitrary as the orientation of the edges. We also present a hierarchical single-strip management strategy for high-performance interactive 3D rendering.