When an agent learns of an expert's credence in a proposition about which they are an expert, the agent should defer to the expert and adopt that credence as their own. This is a popular thought about how agents ought to respond to (ideal) experts. In a Bayesian framework, it is often modelled by endowing the agent with a set of priors that achieves this result. But this model faces a number of challenges, especially when applied to non-ideal agents (who nevertheless interact with ideal experts). I outline these problems, and use them as desiderata for the development of a new model. Taking inspiration from Richard Jeffrey's development of Jeffrey conditioning, I develop a model in which expert reports are taken as exogenous constraints on the agent's posterior probabilities. I show how this model can handle a much wider class of expert reports (for example reports of conditional probabilities), and can be naturally extended to cover propositions for which the agent has no prior.