Highly frequent and highly polysemous verbs, such as give, take, and make, pose a challenge to automatic lexical acquisition methods. These verbs widely participate in multiword predicates (such as light verb constructions, or LVCs), in which they contribute a broad range of figurative meanings that must be recognized. Here we focus on two properties that are key to the computational treatment of LVCs. First, we consider the degree of figurativeness of the semantic contribution of such a verb to the various LVCs it participates in. Second, we explore the patterns of acceptability of LVCs, and their productivity over semantically related combinations. To assess these properties, we develop statistical measures of figurativeness and acceptability that draw on linguistic properties of LVCs. We demonstrate that these corpus-based measures correlate well with human judgments of the relevant property. We also use the acceptability measure to estimate the degree to which a semantic class of nouns can productively form LVCs with a given verb. The linguistically-motivated measures outperform a standard measure for capturing the strength of collocation of these multiword expressions.