One of the insights of dynamic semantics in its various guises (Kamp 1981, Heim 1982, Groenendijk & Stokhof 1991, Kamp & Reyle 1993 among many others) is that interpretation is sensitive to left-to-right order. Is order sensitivity, particularly the default left-to-right order of evaluation, a property of particular meanings of certain lexical items (e.g., dynamically interpreted conjunction) or is it a more general feature of meaning composition? If it is a more general feature of meaning composition, is it a processing (...) ‘preference’ or should it be captured as a ‘harder’ constraint on the type of meanings and operations over meanings involved in natural language interpretation? This squib draws attention to the symmetrical A-too B-too construction (found in a variety of languages, e.g., Hungarian, Japanese, Romanian, Russian) in this context. It argues that any semantic analysis of its main ‘symmetrical-meaning’ characteristic should also allow for subtler interactions between this construction and items that are clearly sensitive to evaluation-order effects, e.g., anaphoric adjectives like next and other. We suggest that the notion of postsupposition embedded in a broader dynamic framework is better able to account for both the symmetric nature of this construction, its non-symmetric variant A-too, and its interaction with items that are evaluation-order sensitive. We briefly compare this proposal with a couple of possible alternative accounts. (shrink)