In this paper I concern myself with The Superman Puzzle (the phenomenon of the substitution failure of co-referential proper names in simple sentences). I argue that the descriptive content associated with proper names, besides determining the proper name's reference, function as truthconditionally relevant adjuncts which can be used to express a manner, reason, goal, time or purpose of action. In that way a sentence with a proper name NN is doing something could be understood as NN is doing something as NN (which means as-so-and-so). I argue that the substitution of names can fail on modified readings because the different descriptive content of proper names modifies the main predicate differently. Here I present a formal representation of modified predicates which allows one to model intuitively the different truth-conditions of sentences from The Puzzle.