Since the emergence of Kayne's (1994) stimulating proposal for an antisymmetric theory of phrase structure and linear order, much work has been devoted to arguing for or against his theory as well as discussing its empirical predictions. As a result, for a number of phenomena involving rightward positioning, such as rightward adjuncts, heavy NP shift, extraposition, postverbal subjects, and postverbal constituents in OV languages, there now exist both an approach consistent with Kayne's theory (the antisymmetric approach) and another not consistent with it (the symmetric approach). In such a situation, it is often difficult to show on empirical grounds that one approach is superior to the other (see Rochemont and Culicover 1997). In what follows, I describe this situation with respect to two well-known phenomena in English: rightward positioning of adjuncts and heavy NP shift. For each of these phenomena, the symmetric and antisymmetric approaches have been proposed, and both approaches can correctly account for the data discussed in previous studies. Here, I examine the approaches from a novel point of view, showing that data involving the licensing of negative polarity items allow us to differentiate them and to decide which is the right one for each of the two empirical domains. Interestingly, the relevant facts lead to different conclusions for the two phenomena. The results have important implications for the antisymmetric view of syntax.