Light verb constructions are a semi-productive class of multiword expression which have not yet been studied computationally in great detail. These constructions combine a restricted set of light verbs (verbs used with a subset of their full semantic features) with a large set of complements; this combination determines the predicate meaning of the expression. In this work we investigate the (semi-)productivity of light verb constructions which employ a predicative noun (a noun that has an argument structure) as their complement. We show that the productivity of these constructions depends on the semantic class of the complement. We develop three novel computational measures for quantifying the acceptability of candidate light verb constructions. Most of these measures meet or exceed the performance of an informed baseline, and reflect distinct trends in productivity along semantic classes and across light verbs. Good correlation and agreement with human judgments of construction acceptability are achieved.