While most vocabulary lists (AWL, GSL, etc.) include only headwords, I believe it would be appropriate to include certain multi-word items. Reasons for their inclusion may be high frequency of occurrence (e.g., phrasal verbs in general English), denoting a specific concept (e.g., supreme court in a list of law words), or evidence that multi-word items are not easily acquired by learners. (I have Japanese learners of English in mind, but any second language learning studies would be useful. Thank you.)