A finite element model is used to study the stresses arising in ceramic matrix composites with different coatings and sliding interfaces. Stress concentrations in the fibers are found near matrix cracks, and their magnitudes depend on the location of the debonded interface and the sliding interfacial shear stress. When debonding occurs away from the fiber surface, fiber flaws are constrained from opening by the coating and fibers are effectively stronger. The probability of flaw failure under the computed stress fields is calculated and used in the Global Load Sharing model to predict composite strength. Results show that composite strength can be optimized by using fibers with a low Weibull modulus m and by designing interfaces with high interfacial shear stress tau, but with debonding away from the fiber/coating interface. These guidelines are consistent with data on "low" strengths in SiC/Glass composites (high m, high tau, fiber/coating debonding) and "high" strengths of SiC/SiC with multilayer coatings (low m, high tau, debonding in coating).