STAIRS is an approach to the compositional development of sequence diagrams supporting the specification of mandatory as well as potential behavior. In order to express the necessary distinction between black-box and glass-box refinement, an extension of the semantic framework with three event messages is introduced. A concrete syntax is also proposed. The proposed extension is especially useful when describing time constraints. The resulting approach, referred to as Timed STAIRS, is formally underpinned by denotational trace semantics. A trace is a sequence built from three kinds of events: events for transmission, reception and consumption. We argue that such traces give the necessary expressiveness to capture the standard UML interpretation of sequence diagrams as well as the black-box interpretation found in classical formal methods.