Complex predicates formed with a semantically bleached verb and a predicating nominal (take a walk) have posed a challenge to grammatical theories. One must explain how the two elements integrate into a semantic and syntactic unit, without losing sight of the lexical constraints the so-called support or light verb constructions are subjected to (*give a jog). In this work, centered on a family of Spanish phrases featuring an emotional state noun and associated with a causative meaning (cf. dar miedo ‘to frighten’, lit. ‘to give fear’), we adopt Goldberg’s (1995, 2006) analysis of “argument structure constructions”, introducing necessary adjustments to fit the composite nature of the predicate, and we show how Cognitive Construction Grammar offers a particularly well-suited model to handle linguistic expressions that combine regular syntactic properties with lexical idiosyncrasies.