We consider the problem of updating arbitrary routes in a software-defined network in a (transiently) loop-free manner. We are interested in fast network updates, i.e., in schedules which minimize the number of interactions (i.e., rounds) between the controller and the network nodes. We first prove that this problem is difficult in general: The problem of deciding whether a k-round schedule exists is NP-complete already for k = 3, and there are problem instances requiring Ω(n) rounds, where n is the network size. Given these negative results, we introduce an attractive, relaxed notion of loopfreedom. We prove that O(log n)-round relaxed loop-free schedules always exist, and can also be computed efficiently.

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