periapsis recession

What would the shape of relativistic corrections to the gravitational potential need to be such that one would observe a periapsis recession instead of a periapsis advance in an orbiting object?

In a picture using corrections to a potential, the decisive change to the Newtonian \(1/r\)-potential is a steepening at small \(r\) caused by general relativity, leading to the periapsis precession. For the opposite to take place, one would needs a shallower potential instead.