While many real-world principal-agent problems have both moral hazard and adverse selection, existing tools largely analyze only one at a time. Do the insights from the separate analyses survive when the frictions are combined? We develop a simple method—decoupling—to study both problems at once. When decoupling works, everything we know from the separate analyses carries over, but interesting interactions also arise. We provide simple tests for whether decoupling is valid. We develop and numerically implement an algorithm to calculate the decoupled solution and check its validity. We also provide primitives for decoupling to work and analyze several extensions.