The interplay between Software Defined Networks (SDN) and Network Function Virtualization (NFV) provides a new networking paradigm where Virtual Network Functions (VNFs) run on physical devices. However, despite the fact that SDN and NFV enable VNFs in the optimal physical device, the optimal physical node may change over time, and the VNFs need to be moved in a seamless and reliable way. Live service migration provides the necessary tools to move virtual resources between physical hosts. The two main virtualization technologies today are virtual machines (VMs) and containers. Containers are known to boot faster than VMs, and thus, lower service downtime in the application. Despite the previous works studying the performance of the live migration process, there are still questions on how the system would behave in a real scenario where conditions are not ideal. To answer those questions, we present in this paper a testbed that performs a container live migration process under tunable conditions, namely image size, network capacity, network load, container’s CPU load and container’s RAM load. We evaluate both migration time and downtime for different configurations of the aforementioned parameters. We use Docker containers and a Python application in the migration process. The results showthat overloading the network can degrade the migration performance remarkably. In contrast, the impact of stressing a container inside a host is marginal.