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Purpose: Measuring the growth of young children's vocabulary is important for researchers seeking to understand language learning as well as for clinicians aiming to identify early deficits. The MacArthur-Bates Communicative Development Inventories (CDIs) are parent report instruments that offer a reliable and valid method for measuring early productive and receptive vocabulary across a number of languages. CDI forms typically include hundreds of words, however, and so the burden of completion is significant. We address this limitation by building on previous work using item response theory (IRT) models to create computer adaptive test (CAT) versions of the CDIs. We created CDI-CATs for both comprehension and production vocabulary, for both American English and Mexican Spanish. Method: Using a data set of 7,633 English-speaking children ages 12-36 months and 1,692 Spanish-speaking children ages 12-30 months, across three CDI forms (Words & Gestures, Words & Sentences, and CDI-III), we found that a 2-parameter logistic IRT model fits well for a majority of the 680 pooled vocabulary items. We conducted CAT simulations on this data set, assessing simulated tests of varying length (25-400 items). Results: Even very short CATs recovered participant abilities very well with little bias across ages. An empirical validation study with N = 204 children ages 15-36 months showed a correlation of r = 0.92 between language ability estimated from full CDI versus CDI-CAT forms. Conclusion: We provide our item bank along with fitted parameters and other details, offer recommendations for how to construct CDI-CATs in new languages, and suggest when this type of assessment may or may not be appropriate.