Parity-odd asymmetries in the electromagnetic decays of compound nuclei can sometimes be amplified above values expected from simple dimensional estimates by the complexity of compound nuclear states. Using a statistical approach, we estimate the root-mean-square of the distribution of expected parity-odd correlations s n · k γ , where s n is the neutron spin and k γ is the momentum of the γ , in the integrated γ spectrum from the capture of cold polarized neutrons on Al, Cu, and In. We present measurements of the asymmetries in these and other nuclei. Based on our calculations, large enhancements of asymmetries were not predicted for the studied nuclei and the statistical estimates are consistent with our measured upper bounds on the asymmetries.