Abstract: We discuss dilaton gravity with potentials that are deformed away from JT gravity. We discuss semi-classical solutions with these potentials and elucidate new complex saddles at fixed energy which contribute to the density of states. We also discuss how to reproduce the semi-classical limit of a formula for the density of states first derived by using the connection between minimal string theory and dilaton gravity. In this connection, the perturbative expansion in the deformation parameter corresponds to a gas of defects in rigid AdS_2. We highlight an interesting effect wherein, at leading order in the semi-classical expansion, this perturbative series in the deformation parameter truncates at finite order.