In a recent paper, Jaggi et al., presented a distributed polynomial-time rate-optimal network-coding scheme that works in the presence of Byzantine faults.We revisit their adversarial models and augment them with three, arguably realistic, models. In each of the models, we present a distributed scheme that demonstrates the usefulness of the model. In particular, all of the schemes obtain optimal rate C-z, where C is the network capacity and z is a bound on the number of links controlled by the adversary.