Prior research shows that languages balance syntactic complexityagainst morphological complexity. We explore this relationshipusing a new measure of syntactic complexity, functionalindeterminacy, which measures the aggregate uncertainty ofmapping from lexical items to syntactic function. We predict thatgreater functional indeterminacy for nouns will correlate withlanguages having case systems, and for those with case systems,increased number of cases. We operationalize indeterminacy as thesimple and normalized conditional entropies of the summedfrequency distributions of nouns across syntactic dependencies. Wecompute these measures for 44 languages. We then correlate themeasures with presence and number of cases in two regressionanalyses, controlling for genetic affiliation between languages.Results show that as the functional indeterminacy of nounsincreases, languages are more likely to have case systems, and ifso, to have more cases. These data provide new support for thefunctionally motivated relationship between morphological andsyntactic complexity.