Lexical competence is considered to be an essential step in the development and consolidation of a student's linguistic ability, and thus the reliable assessment of such competence turns out to be a fundamental aspect in this process. The design and construction of vocabulary tests has become an area of special interest, as it may provide teachers with accurate instruments to evaluate students' learning process and their linguistic needs. This paper describes the design, construction and implementation of a computer-adaptive vocabulary test for the assessment of those students taking the virtual course ADELEX (Assessing and Developing Lexical Competence on the Internet) at the University of Granada (Spain). The test was first developed as a paper-and-pencil version, followed by a first-generation test--"conventional" or "linear" test, which presents all test takers with the same items in the same sequence; and eventually the second-generation test--"computer-adaptive" test (CAT), which provides each test taker with a unique tailor-made measurement for achieving valid and reliable vocabulary assessment. (Contains 2 figures, 1 table, and 9 notes.)