Although recent spectroscopic studies of chemically denatured proteins hint at significant nonrandom residual structure, the results of extensive small angle X-ray scattering studies suggest random coil behavior, calling for a coherent understanding of these seemingly contradicting observations. Here, we report the results of a Monte Carlo study of the effects of two types of local structures, alpha helix and Polyproline II (PPII) helix, on the dimensions of random coil polyalanine chains viewed as a model of highly denatured proteins. We find that although Flory's power law scaling, long regarded as a signature of random coil behavior, holds for chains containing up to 90% alpha or PPII helix, the absolute magnitude of the chain dimensions is sensitive to helix content. As residual alpha helix content increases, the chain contracts until it reaches a minimum radius at approximately 70% helix, after which the chain dimensions expand rapidly. With an alpha helix content of approximately 20%, corresponding to the Ramachandran probability of being in the helical basin, experimentally observed radii of gyration are recovered. Experimental radii are similarly recovered at an alpha helix content of approximately 87%, providing an explanation for the previously puzzling experimental finding that the dimensions of the highly helical methanol-induced unfolded state are experimentally indistinguishable from those of the helix-poor urea-unfolded state. In contrast, the radius of gyration increases monotonically with increasing PPII content, and is always more expanded than the dimensions observed experimentally. These results suggest that PPII is unlikely the sole, dominant preferred conformation for unfolded proteins.