George Gaylord Simpson famously postulated that much of life's diversity originated as adaptive radiations—more or less simultaneous divergences of numerous lines from a single ancestral adaptive type. However, identifying adaptive radiations has proven difficult due to a lack of broad-scale comparative datasets. Here, we use phylogenetic comparative data on body size and shape in a diversity of animal clades to test a key model of adaptive radiation, in which initially rapid morphological evolution is followed by relative stasis. We compared the fit of this model to both single selective peak and random walk models. We found little support for the early-burst model of adaptive radiation, whereas both other models, particularly that of selective peaks, were commonly supported. In addition, we found that the net rate of morphological evolution varied inversely with clade age. The youngest clades appear to evolve most rapidly because long-term change typically does not attain the amount of divergence predicted from rates measured over short time scales. Across our entire analysis, the dominant pattern was one of constraints shaping evolution continually through time rather than rapid evolution followed by stasis. We suggest that the classical model of adaptive radiation, where morphological evolution is initially rapid and slows through time, may be rare in comparative data.