The design of Lyot-stop systems in earth limb viewing radiometers is first reviewed, with particular reference to the stray-light analysis methods used for instrument design and performance evaluation. These methods are given in order of increasing sophistication, up to the most powerful technique for diffraction analysis, that of generalized beam propagation analysis. The typical design features of radiometers for the limb-viewing application are discussed to summarize the important stray-light issues, including scatter, ghosting, and diffraction effects. How for multichannel instruments based on arrays of detectors, the interplay of these issues affects the Lyot-stop system is shown, pushing the design toward nonstandard geometries for which the generalized analysis method becomes essential. An example is given of the use of the technique in a system requiring a nonstandard Lyot-stop geometry, including the computation of the full diffracted energy patterns at each stage of the Lyot-stop system, illustrating the physics of the diffraction suppression, and giving insight into the design trade-offs; in particular, that between signal throughput and diffraction rejection. For one choice of this trade-off, the net diffraction response is calculated. This quantity is an important input to the ground characterization of the predicted performance.