We study a principal-agent model with moral hazard and adverse selection. Agents have private
information about the distribution of outputs conditional on each effort and, possibly, the cost of effort.
We prove existence, characterize the solution, and establish several general properties of the resulting
multidimensional screening problem. A positive mass of types with low conditional probabilities of
success gets a constant payment and zero rents. Exclusion is desirable if and only if it is first-best
efficient. Unlike in pure adverse selection models, there is distortion everywhere: the region of types
who exert high effort is contained in the interior of the first-best high-effort region. Under additional
conditions, the optimal mechanism offers only finitely many contracts. For example, if the agent is
risk neutral and has limited liability, all agents are offered a single contract. Our model, therefore,
provides a multidimensional screening rationale for the lack of rich menus of contracts observed in
certain environments. We apply our framework to multidimensional generalizations of canonical
models in insurance, regulation, and optimal taxation and show that it generates novel results.