This paper studies adverse selection problems with a one-dimensional principal instrument and a two-dimensional agent type.
We provide an optimality condition that characterizes the bunching of types that allows us to obtain analytical solutions for examples from the literature and for a new example that is far from the linear-quadratic case.

Additionally, by comparing types by their marginal valuation for the instrument, we reduce the number of incentive compatibility constraints, thus making the discretized problem computationally tractable for relatively fine discretizations.