A decade ago we introduced empirically derived formulas which allowed one to estimate the performance which can be achieved in the design of broad-band antireflection (AR) coatings based upon the indices of refraction of the materials to used, the bandwidth required, and the overall thickness of the coating. This has proved to be a useful tool to avoid attempting impossible designs and to guide the designer toward an optical result. It can also be helpful to non-designers who need to know what can and cannot be done before specifying a system AR coating requirement. In the new work reported here, forumlas with additional accuracy have been developed by further data generation and the application of modern statistical analysis tools. The overall thickness parameter used in the equations has also been better defined and understood, and the tendency of overall thicknesses to have quantization has been studied further. These findings are discussed in conventional thin film design terms and also from the Fourier synthesis/analysis viewpoint.