© 2015 Elsevier Ltd. In the Barber-Pole Illusion (BPI), a diagonally moving grating is perceived as moving vertically because of the narrow, vertical, rectangular shape of the aperture window through which it is viewed. This strong shape-motion interaction persists through a wide range of parametric variations in the shape of the window, the spatial and temporal frequencies of the moving grating, the contrast of the moving grating, complex variations in the composition of the grating and window shape, and the duration of viewing. It is widely believed that end-stop-feature (third-order) motion computations determine the BPI, and that Fourier motion-energy (first-order) computations determine failures of the BPI. Here we show that the BPI is more complex: (1) In a wide variety of conditions, weak-feature stimuli (extremely fast, low contrast gratings, 21.5. Hz, 4% contrast) that stimulate only the Fourier (first-order) motion system actually produce a slightly better BPI illusion than classical strong-feature gratings (2.75. Hz, 32% contrast). (2) Reverse-phi barber-pole stimuli are seen exclusively in the feature (third-order) BPI direction when presented at 2.75. Hz and exclusively in the opposite (Fourier, first-order) BPI direction at 21.5. Hz, indicating that both the first- and the third-order systems can produce the BPI. (3) The BPI in barber poles with scalloped aperture boundaries is much weaker than in normal straight-edge barber poles for 2.75. Hz stimuli but not in 21.5. Hz stimuli. Conclusions: Both first-order and third-order stimuli produce strong BPIs. In some stimuli, local Fourier motion-energy (first-order) produces the BPI via a subsequent motion-path-integration computation (Journal of Vision (2014) 14, 1--27); in other stimuli, the BPI is determined by various feature (third-order) motion inputs; in most stimuli, the BPI involves combinations of both. High temporal frequency, low-contrast stimuli favor the first-order motion-path-integration computation; low temporal frequency, high-contrast stimuli favor third-order motion computations.