C-tests are a specific variant of cloze tests that are considered time-efficient, valid indicators of general language proficiency. They are commonly analyzed with models of item response theory assuming local item independence. In this article we estimated local interdependencies for 12 C-tests and compared the changes in item difficulties, reliability estimates, and person parameter estimates for different modeling approaches: (a) Rasch, (b) testlet, (c) partial credit, and (d) copula models. The results are complemented with findings of a simulation study in which sample size, number of testlets, and strength of residual correlations between items were systematically manipulated. Results are discussed with regard to the pivotal question whether residual dependencies between items are an artifact or part of the construct.