Triggered Message Sequence Charts (TMSCs) are a visual, mathematically precise notation for capturing system requirements as conditional and partial scenarios. This paper shows how TMSCs may be used to formalize two different requirements modeling methodologies. The first approach combines prescriptive ("do this") and constraint-based ("don?t do that") requirements within a single specification; it is useful for composing localized subsystem requirements with global system ones. The second approach supports layered specifications in which partial descriptions of requirements may be elaborated on in a succession of steps; it is suitable for the incremental development of complex behavior in which "error" scenarios are "layered on top of" normative ones. Both methodologies derive their formal robustness from the notion of semantic refinement for TMSCs, which is based on DeNicola?s and Hennessy?s must preorder. Case studies are used to illustrate the utility of the work.