This paper compares two competing theories about numeral classifiers drawing on data from fieldwork from three languages, Ch’ol (Mayan, Mexico), Shan (Tai-Kadai, Thailand), and Chuj (Mayan, Guatemala). We discuss CLASSIFIER-FOR-NUMERAL theories and CLASSIFIER-FOR-NOUN theories, which we argue make different predictions based on the assumed semantic contribution of the classifier in each set of theories. We argue that both these theories can account for data exhibited in typologically diverse languages. We argue that Ch’ol is an example of a classifier-for-numeral language and Shan is a classifier-for-noun language. Furthermore, we argue that Chuj has two kinds of classifiers: a numeral classifier that patterns with Ch’ol’s classifiers-for-numerals and a noun classifier that has some overlap with Shan’s classifiers-for-nouns. The Chuj noun classifier appears to have a similar syntactic position compared with the Shan classifier and is associated with specificity/definiteness presuppositions, as has been argued for other Southeast Asian classifier languages (Simpson & Ngo 2018, Vietnamese).