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The optimal spectral sampling (OSS) method provides a fast and accurate way to model radiometric observations and their Jacobians (required for inversion problems) as a linear combination of monochromatic quantities. The method is flexible and versatile with respect to the treatment of variable constituents, and the method's fidelity to reference line-by-line (LBL) calculations is tunable. The focus of this paper is on the modeling of radiances from hyperspectral infrared sounders in both clear and cloudy (scattering) atmospheres for application to retrieval and data assimilation. In earlier articles, the authors presented an approach that performed spectral sampling for each channel sequentially. This approach is particularly robust in terms of preserving fidelity to LBL models and yields ratios of monochromatic calculations per channel of approximately 1:1 for such hyperspectral sensors as the Infrared Atmospheric Sounding Interferometer (IASI) or the Atmospheric Infrared Sounder (AIRS) (when tuned for nominal 0.05-K accuracy). This paper describes the generalization of the OSS concept to minimize the total number of monochromatic points required to model a set of channels across individual spectral bands or across the entire domain of the measurements. Its application to principal components of radiance measurements is addressed. It is found that the optimal solution produced by the OSS method offers computational advantages over existing models based on principal components, but, more importantly, it has superior error characteristics. [ABSTRACT FROM AUTHOR]