In second language (L2) vocabulary studies there is continuing interest in tests of depth of vocabulary knowledge, measuring various aspects of word knowledge other than just the form--meaning link that is the focus of breadth (or size) tests. This study aimed to explore new formats that could be used as diagnostic tools for assessing depth of academic vocabulary knowledge. The participants were 222 first-year students taking a programme of English for academic purposes (EAP) at a university in Vietnam. The depth measure was a newly developed test of a sample of words from Gardner and Davies' Academic Vocabulary List, including sub-tests on receptive knowledge of synonyms, collocations and word parts. The participants also took the Updated Vocabulary Levels Test as a breadth measure, as well as a translation test. Results showed that most of the students had a relatively limited knowledge of general English vocabulary. There was a moderate correlation between the breadth and depth tests. The students had the best knowledge of synonyms, followed by word parts and then collocations. The collocation and word parts sub-tests included a Not Sure option to discourage blind guessing, and analyses of responses to this option offered useful insights into the students' test-taking behaviour.