Automated user-interface generation environments have been criticized for their failure to deliver rich and powerful interactive applications [18]. To specify more powerful systems, designers require multiple specialized modeling notations [12, 14]. The model-composition problem is concerned with automatically deriving powerful, correct, and efficient user interfaces from multiple models specified in different notations. Solutions balance the advantages of separating code generation into specialized code generators with deep, model-specific knowledge against the correctness and efficiency obstacles that result from such separation. We present a correct and efficient solution that maximizes the advantage of separation through run-time composition mechanisms.