Principal-agent models are pervasive in theoretical and applied economics, but their analysis has largely been limited to the "first-order approach" (FOA) where incentive compatibility is replaced by a first-order condition. This paper presents a new approach to solving a wide class of principal-agent problems that satisfy the monotone likelihood ratio property but may fail to meet the requirements of the FOA. Our approach solves the problem via tackling a max-min-max formulation over agent actions, alternate best responses by the agent, and contracts.