In 1978, Salam and Strathdee suggested on the basis of Froissart boundedness that curvature-squared terms should be included in the gravitational Lagrangian. Despite the presence of ghosts in such theories, the subject has remained a persistent topic in approaches to quantum gravity and cosmology. In this article, the space of spherically symmetric solutions to such theories is explored, highlighting horizonless solutions, wormholes and non-Schwarzschild black holes.