Abstract: The saddle-point approximation often used to make sense of path integrals is especially subtle when gravity is dynamical, most notably because of the conformal factor problem which renders the action unbounded below. In this talk I will discuss two aspects of saddle points in axion gravity, making use of the dual description in terms of a 3-form flux: (i) how Picard-Lefschetz theory can be used to identify in a democratic way which Lorentzian, complex and Euclidean saddle points contribute to Lorentzian path integrals, and (ii) the perturbative stability of the Giddings-Strominger Euclidean wormhole. Based on [2203.01956] with Gary Shiu and Nidhi Sudhir.