According to recent proposals in formal syntax, the left-most position in the C(omplementizer)-layer is dedicated to the representation of the context of utterance (call this hypothesis LP). This idea has had little impact on semantic theories of indexicals. The reason is that indexicals are regarded, after Kaplan’s (1989) Logic of Demonstratives (LD), as directly referential and rigid. However, the phenomenon of shifted indexicality (Schlenker 2004) cast doubts on LD and, in particular, on the assumption that the descriptive content of indexical terms has no truth-conditional importance. Any extension (or reformulation) of LD that meets this empirical challenge must in fact allow the descriptive content of indexicals to interact with scope taking operators such as verba dicendi. Moreover, such a theory must account for the restrictions on these interactions. For instance, shifting-friendly languages allow indexicals to shift only in the scope of specific verbs (Anand 2006). In this contribution we show that LP offers an empirically adequate account of indexical shifting. We propose that: (a) indexical features (such as first-person features) are presuppositional; (b) indexicals features are hosted in the position in the left-periphery that is devoted to the representation of the context of utterance. The proposal shows that a presuppositional analysis is able to provide an elegant modeling of the indexical shifting, if we are ready to develop the basic insight that syntax has precise ways to encode presuppositional values and their locus of resolution. Furthermore, our syntax-oriented presuppositional approach makes good prospects for individuating the logical roots of two-dimensionalism in the semantics of indexicals, in a theory-independent way.