We present models of the spectral reflectances of groups of outer Solar System objects defined primarily by their colors in the spectral region 0.4 -1.2 microns, and which have geometric albedo 0.04 at wavelength 0.55 microns. Our models of the groups with the strongest reflectance gradients (reddest colors) use combinations of organic tholins. We test the hypothesis that metal-reddened igneous rock-forming minerals contribute to the red colors of Centaurs and KBOs by using the space-weathered lunar soil as one of the components of our models. We find that our models can admit the presence of moderate amounts of space-weathered (metal-reddened) minerals, but that they do not require this material to achieve the red colors of the reddest outer Solar System bodies. Our models with organic tholins are consistent with the results of other investigators.