Ever since Eldredge and Gould proposed their model of punctuated equilibria, evolutionary biologists have debated how often this model is the best description of nature and how important it is compared to the more gradual models of evolution expected from natural selection and the neo-Darwinian paradigm. Recently, Cubo proposed a method to test whether morphological data in extant ratites are more compatible with a gradual or with a speciational model (close to the punctuated equilibrium model). As shown by our simulations, a new method to test the mode of evolution of characters (involving regression of standardized contrasts on their expected standard deviation) is easier to implement and more powerful than the previously proposed method, but the Mesquite module CoMET (aimed at investigating evolutionary models using comparative data) performs better still. Uncertainties in branch length estimates are probably the largest source of potential error. Cubo hypothesized that heterochronic mechanisms may underlie morphological changes in bone shape during the evolution of ratites. He predicted that the outcome of these changes may be consistent with a speciational model of character evolution because heterochronic changes can be instantaneous in terms of geological time. Analysis of a more extensive dataset confirms his prediction despite branch length uncertainties: evolution in ratites has been mostly speciational for shape-related characters. However, it has been mostly gradual for size-related ones.