Descriptions of realized variations, correlations, and covariations among physical attributes (phenotypic integration) provide a useful framework for understanding evolutionary pathways and the generation of diversity. The ability of many birds to see near-ultraviolet (UV) light, which is invisible to normal humans, has focused attention on special properties of ‘hidden’ UV plumage signals. Little is known, however, about associations between UV (320–400 nm) and longer-wavelength visible (400–700 nm) reflectance, or how such patterns compare to those among longer-wavelength visible reflectance components alone. Analysis of physical reflectance from most carotenoid-bearing yellow, orange, and red plumage patches of male tanager-finch (Thraupini, Emberizinae) species revealed that amounts of longer-wavelength visible and UV reflectance components expressed different patterns of covariation with the spectral location of the main longer-wavelength visible reflectance band (cut-off wavelength, associated with ‘redness’). Longer-wavelength visible components were linear (y = x) functions of cut-off wavelength, whereas UV components were nonlinear cubic polynomial (y = x3 − x2 + x) functions of cut-off wavelength. The more complex UV-related patterns consisted essentially of two parallel curves partially separated by a gap such that: (1) each curve was associated with a different family of carotenoid pigments and was centred at different (relatively shorter versus longer) cut-off wavelengths; (2) each curve described a negative relationship between the amount of UV and the cut-off wavelength; (3) modifications to feather branching structure tracked the negative trend of each curve; (4) the gap between curves existed because plumages with intermediate cut-off wavelengths lacked moderate to high UV reflectance; and (5) functional relationships persisted when phylogeny and other confounding effects (age of study skin, breeding season) were taken into account. Thus, phenotypic integration between UV and long-wavelength visible reflectance can be just as distinctive as reflectance patterns restricted to the UV. Moreover, by contrast to the view that plumage ornaments are relatively unconstrained aspects of morphology, the highly regular phenotypic patterns expressed by carotenoid-bearing plumages suggest that reflectance evolves within specific limits, even in the context of an extensive ecological radiation. Indeed, the near-exhaustive sampling of taxa implies that gaps in the observed phenotype space correspond to plumages that have not evolved in this avian clade. Much of the curve/gap structure is consistent with what is known about the physics, chemistry, and metabolism of carotenoids in these or related birds, including, for example, that only certain subclasses of carotenoids are used for plumage displays. The key contribution that UV makes to the expression of these patterns suggests that avian UV sensitivity enhances the information content and honesty of carotenoid-bearing plumage signals compared to what humans perceive. The structure of phenotype space reveals that a complex interplay between extrinsic (dietary, ecological) and intrinsic (physico-chemical, physiologic) factors ultimately determines plumage variation. © 2008 The Linnean Society of London, Biological Journal of the Linnean Society, 2008, 93, 89–109.