Item-response theory (IRT) models are test-theoretical models with many practical implications for educational measurement. For example, test-linking procedures and large-scale educational studies often build on IRT frameworks. However, IRT models have been rarely applied to divergent thinking which is one of the most important indicators of creative potential. This is most likely due to the fact that the best-known models, such as the one-parameter logistic Rasch model, can be only used for binary data. But its less known, and often overlooked, predecessor, the Rasch Poisson count model (RPCM), is well suited to model many important divergent-thinking outcomes such as fluency. In the current study we assessed RPCM fit to four different divergent thinking tasks. We further assessed the fit of the data to a two-dimensional variant of the RPCM to take into account construct differences due to verbal and figural task modality. We also compared estimated measurement precision based on the two-dimensional model, two separately estimated modality-specific unidimensional models, and a classic approach. The results indicated that the two-dimensional approach was advantageous, especially when correlations of latent variables are of interest. The RPCM and its more flexible multidimensional variants are discussed as a psychometric tool which possibly directs future research towards a better understanding of all the available divergent-thinking tasks.