As measures of general language proficiency, C-tests are ubiquitous in language testing. Speeded C-tests are quite recent developments in the field and are deemed to be more discriminatory and provide more accurate diagnostic information than power C-tests especially with highability participants. Item response theory modeling of speeded C-tests has not been discussed in the literature, and current approaches for power C-tests based on ordinal models either violate the model assumptions or are relatively complex to be reliably fitted with small samples. Count data models are viable alternatives with less restrictive assumptions and lower complexity. In the current study, we compare count data models with commonly applied ordinal models for modeling a speeded C-test. It was found that a flexible count data model fits equally well in absolute and relative terms as compared with ordinal models. Implications and feasibility of count data models for the psychometric modeling of C-tests are discussed.