This article discusses in detail two cases of even-marked negative polarity items (NPIs) in Greek and Korean that are not scalar or exhaustive. This prima facie paradoxical finding suggests that even-marking is not always an indicator of scalarity—and, at least in the case of the Korean and Greek NPIs discussed, even is grammaticalized as a nonscalar NPI marker. We propose that the nonscalar NPIs are antispecific indefinites with referential vagueness, which is a form of ignorance best captured as nonexhaustive variation in the potential values of the NPIs (Giannakidou & Quer 2013). We also show that the difference in Greek and Korean between scalar and nonscalar NPIs is reflected in prosody: scalar NPIs are ‘emphatic’, and nonscalar NPIs are ‘non-emphatic’; we therefore conclude that prosodic prominence, not even, signals scalar structure. The fact that not all NPIs are scalar or exhaustive falsifies theories claiming that exhaustivity is the source of all NPIs (Chierchia 2006, 2013).