In this paper, we make a case for using lightweight containers for fine-grained resource flexing for Virtualized Network Functions (VNFs) to meet the demands of varying workloads. We quantitatively compare the VNF performance and infrastructure resource usage of three instantiations (bare metal, virtual machine, and container) of three selected VNFs. The three VNFs we experiment with are the Mobility Management Entity (MME) of the Evolved packet core (EPC) architecture for cellular networks, the Suricata multi-threaded Intrusion Detection System (IDS), and the Snort single-threaded IDS. Our results show that container-based instantiations not only incur lower resource usage but also have shorter boot time. This makes containers an attractive choice for fine-grained VNF resource flexing. The lessons learned from our empirical case studies with EPC and IDS provide important guidelines for building an elastic micro-service architecture for NFV deployments.