Accretionary outlines of many brachiopods are closely matched by one or more episodes of logarithmic spiral growth where each episode has a constant growth gradient. An episodic model supports the observations of abrupt change, but not that of gradual change in accretionary growth. A reliable guide to the number of growth episodes is given by the pattern of residuals after fitting a single spiral to an outline. An episodic model exposes subtle variations in growth that are not easily described by visual examination. A three-episode model clarifies a shape difference between two species of the endemic New Zealand genus Neothyris. Direct observation, along with linear measurements and their ratios, was unable to pinpoint that the well-documented dorsoventral compression in one species arises from a growth episode in the ventral valve. Logarithmic spirals about a single coiling axis are not suited for large, disjunct changes in outline for which the moving-frame methods or aperture-deposition models are applicable.