Containers are quickly increasing in popularity as the mechanism to deploy computation in the cloud. In order to provide consistent and reliable performance, cloud providers must ensure containers cannot adversely interfere with one another. Because containers share the same underlying OS, it is more challenging to provide isolation in a container-based framework than a traditional VM-based framework. And while many schemes can isolate CPU, memory, disk, or network bandwidth in multi-tenant environments, less attention has been paid to how the time spent processing network traffic affects isolation on the host server. This paper shows computational overhead associated with the network stack can break isolation in container-based environments. Specifically, a container with heavy network traffic can decrease the computation available to other containers sharing the same server. We propose a scheme, called Iron, that accounts for the time spent in the networking stack on behalf of a container and ensures this processing cannot adversely impact colocated containers through novel enforcement mechanisms. Our results show Iron effectively provides isolation under realistic and adversarial conditions, limiting interference-based slowdowns as high as 6× to less than 5%.