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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 highlight and exploit this linear order in efficient triangle-strip management for high-performance rendering. We present new algorithms to generate weighted single-strip representations that respect different constraint-based clustering of triangles. These functional constraints can be application dependent; for example, normal-based constraints for efficient visibility culling or spatial constraints for highly coherent vertex-caching. We also present a hierarchical single-strip-management strategy for high-performance interactive 3D rendering.