The three-tiered discourse representation defined in (Luperfoy, 1991) is applied to multimodal humancomputer interface (HCI) dialogues. In the applied system the three fiers are (1) a linguistic analysis (morphological, syntactic, sentential semantic) of input and output communicative events including keyboard-entered command language atoms, NL strings, mouse clicks, output text strings, and output graphical events; (2) a discourse model representation containing one discourse object, called a peg, for each construct (each guise of an individual) under discussion; and (3) the knowledge base (KB) representation of the computer agent's 'belief' system which is used to support its interpretation procedures. I present evidence to justify the added complexity of this three-tiered system over standard two-tiered representations, based on (A) cognitive processes that must be supported for any non-idealized dialogue environment (e.g., the agents can discuss constructs not present in their current belief systems), including information decay, and the need for a distinction between understanding a discourse and believing the information content of a discourse; (B) linguistic phenomena, in particular, context-dependent NPs, which can be partially or totally anaphoric; and (C) observed requirements of three implemented HCI dialogue systems that have employed this three-tiered discourse representation.