In this paper, we introduce a class of exceptionally narrow-scoping singular indefinites in English (e.g., “Sam drove a car for several years before switching to a truck”), which pattern more closely with what have been termed “weak definites” in the literature (e.g., Poesio, 1994; Carlson et al., 2006) than with regular indefinites. While the existence of such exceptional “weak” indefinites has been previously anticipated by Klein et al. (2013), the category is difficult to distinguish from simple narrow-scoped singular indefinites in most contexts. Here, we argue that there is one environment where weak singular indefinites can be distinctively identified: namely, when they appear with for-adverbials. We sketch a concrete implementation of a semantic incorporation-based account for such nominals, bringing them analytically in line with incorporation analyses of weak definites, building closely on the ideas in Dayal (2011). We further briefly discuss how the proposed analysis adjudicates between two competing analyses for for-adverbials, one which assumes that for encodes a universal quantifier (e.g., Deo & Piñango, 2011) and another which takes for to be non-quantificational (e.g., Champollion, 2013), in favor of the latter view. We close by considering some remaining issues surrounding semantically incorporated DPs in English: specifically, how weak (in) definites relate to other nominals that receive covarying interpretations across contexts—such as bare plurals on the one hand (which we do not take to be semantically incorporated) and bare singulars on the other.