Among the most ornate animal traits in nature are the angle-dependent (i.e. iridescent) structural colors of many birds, beetles, and butterflies. Though we now have a solid understanding of the mechanisms, function, and evolution of these features in several groups, less attention has been paid to the potential for angle-dependent reflectance in otherwise matte-appearing (i.e. not thought to be structurally colored) tissues. Here for the first time we describe non-iridescent angle-dependent coloration from the tail and wing feathers of several parrot species (Psittaciformes). We employed a novel approach \u2014 by calculating chromatic and achromatic contrasts (in just noticeable differences, JNDs) of straight and angled measurements of the same feather patch \u2014 to test for perceptually relevant angle-dependent changes in coloration on dorsal and ventral feather surfaces. We found, among the 15 parrot species studied, significant angle dependence for nearly all parameters (except chromatic JNDs on the ventral side of wing feathers). We then measured microstructural features on each side of feathers, including size and color of barbs and barbules, to attempt to predict interspecific variation in degree of angle-dependent reflectance. We found that hue, saturation, and brightness of feather barbs, barbule saturation, and barb:barbule coverage ratio were the strongest predictors of angle-dependent coloration. Interestingly, there was significant phylogenetic signal in only one of the seven angle-dependence models tested. These findings deepen our views on the importance of microscopic feather features in the production of directional animal coloration, especially in tissues that appear to be statically colored.