In Norwegian, a weak quantifier or a scalar adjective with a positive value may combine with a definite noun and thereby form an attenuating NPI. These phrases, which I call predicative definite NPIs, are exceptional as nominal phrases, since they do not accept a prenominal definiteness marker despite their overall definiteness, and they are exceptional as attenuating NPIs, since they are templatic instead of being lexically defined.<br />The reason why predicative definite NPIs do not accept prenominal definiteness markers is arguably that there is no D head. The absence of a D head makes the phrases defective in their ability to refer. Hence, they are semantically predicative, and in the terms of Giannakidou (1998) they are referentially dependent, which is a property that characterises many NPIs in general. Hence, the lack of a D head causes the phrases to be NPIs, despite their definiteness.<br />Concerning their licensing properties, when three influential theories of NPIlicensing&mdash;Progovac (1994), van der Wouden (1997) and Giannakidou (1998)&mdash; are confronted with the NPIs discussed here, it appears that Giannakidou&rsquo;s model more successfully than the others can capture the licensing of predicative definite NPIs, although some refinement is required even here.