ModelFinder is a fast and flexible model-selection method for molecular phylogenetic analysis, designed to improve the accuracy of phylogenetic estimates. It incorporates a flexible rate-heterogeneity-across-sites (RHAS) model, allowing for concurrent searches of model-space and tree-space. The method uses the expectation-maximization (EM) algorithm to estimate parameters of the probability distribution-free (PDF) model of RHAS, which can capture more complex rate distributions than traditional discrete Γ distributions. ModelFinder is implemented in IQ-TREE and offers advanced features such as the ability to compare models on different trees and the inclusion of the PDF model. Evaluations using simulated and real data show that ModelFinder is accurate and often outperforms other model-selection methods in terms of the fit between tree, model, and data. The method is particularly useful for alignments with complex evolutionary histories and can detect models that other methods might miss.ModelFinder is a fast and flexible model-selection method for molecular phylogenetic analysis, designed to improve the accuracy of phylogenetic estimates. It incorporates a flexible rate-heterogeneity-across-sites (RHAS) model, allowing for concurrent searches of model-space and tree-space. The method uses the expectation-maximization (EM) algorithm to estimate parameters of the probability distribution-free (PDF) model of RHAS, which can capture more complex rate distributions than traditional discrete Γ distributions. ModelFinder is implemented in IQ-TREE and offers advanced features such as the ability to compare models on different trees and the inclusion of the PDF model. Evaluations using simulated and real data show that ModelFinder is accurate and often outperforms other model-selection methods in terms of the fit between tree, model, and data. The method is particularly useful for alignments with complex evolutionary histories and can detect models that other methods might miss.