We analyze resilient protocols over noisy networks, focusing on the interesting setting where $n$ computing parties (clients) are supported by a set of $k$ assisting servers. All communication links suffer from random noise, and the goal is to design noise-resilient computations with low round-complexity compared to the noiseless case. We give tight bounds for the case where a constant number of servers is present. We show that $\Theta(\log n)$ rounds are necessary and sufficient to compute any non-constant function of the clients' inputs, with error probability tending to~0. We further show a lower bound of $\Omega(\log n/k)$ rounds, for networks with $k< O(\log n)$ servers. This lower bound suggests that additional assisting servers could help reducing the overall round complexity.