Sensitivity to visual motion is a fundamental property of neurons in the visual cortex and has received wide attention in terms of mathematical models.Akey feature of many popular models for cortical motion sensors is the use of pairs of functions that are related by a 90° phase shift. This phase relationship, known as quadrature, is the hallmark of the motion energy model and played an important role in the development of a class of model dubbed elaborated Reichardt detectors. For decades, the literature has supported a link between quadrature and the observation that motion detectors and human observers often prefer a 1/4 cycle displacement of an apparent motion stimulus that consists of a pair of sinusoidal gratings. We show that there is essentially no link between quadrature and this preference. Quadrature is neither necessary nor sufficient for a motion sensor to prefer 1/4 cycle displacement, and motion energy is not maximized for a 1/4 cycle step. Other properties of motion sensors are the key: the opponent subtraction of two oppositely tuned stages that individually have sinusoidal displacement tuning curves. Thus, psychophysical and neurophysiological data revealing a preference at or near 1/4 cycle displacement do not offer specific support for common quadrature or energy-based motion models. Instead, they point to a broader class of model.