Faults in an IP network have various causes such as the failure of one or more routers at the IP layer, fiber-cuts, failure of physical elements at the optical layer, or extraneous causes like power outages. These faults are usually detected as failures of a set of dependent logical entities--the IP links affected by the failed components. We present Shrink, a tool for root cause analysis of network faults which, given a set of failed IP links, identifies the underlying cause of the faulty state. Shrink models the diagnosis problem as a Bayesian network. It has two main contributions. First, it effectively accounts for noisy measurement and inaccurate mapping between the IP and optical layers. Second, it has an efficient inference algorithm that finds the most likely failure causes in polynomial time and with bounded errors. We compare Shrink with two prior approaches and show that it substantially improves the performance.