This paper deals with a class of non-canonical construct state nominals, whose annex is non-nominal. More specifically, it examines the properties these non-canonical constructs share with canonical construct state nominals, including the absence of overt definiteness marking on the head noun. Non-canonical construct state nominals also differ from canonical construct states in imposing a restriction on the categorial nature of the annex. I argue that a predication structure (Den Dikken 2006, Ouhalla 2011) underlies non-canonical constructs, where the annex is the subject of predication and the head, a 'minimal np', is the predicate, which raises over its subject. This analysis, which seems to invert the expected subject-predicate relation within construct states, is shown to account for a number of new observations related to the structural properties of non-canonical constructs. Non-canonical construct states alternate with constructions where the head noun does not appear in construct form and can take the definite marker. I argue that those alternate constructions are in fact derived from a different initial predication structure, where the head noun is in fact the subject of predication. Being a 'minimal np', the head of non-canonical constructs cannot bear definiteness marking, under the assumption that the definite article is the overt expression of D[Def], Therefore, the account for the distribution of overt definite marking is reduced to whether the outer D dominating the whole construct state is overtly expressed. I argue that a definite outer D is not expressed in non-canonical construct states due to the Doubly-filled Comp Filter (dfcf) generalized to specifier-head configurations, as in Koopman (2000). [ABSTRACT FROM AUTHOR]