  We give an upper bound on the number of exceptional orthogonal projections of
a small set of points in a plane over a prime order field, which makes progress
toward a conjecture of Chen (2018). This theorem relies on a new upper bound on
the number of incidences between an arbitrary set of lines and a set of points
contained in a reasonably small pencil of lines. We also prove a new upper
bound on the number of incidences between points and lines when both are
Cartesian products in an appropriate sense.
