Serverless computing is a popular cloud computing paradigm, which requires low response latency to handle on-demand user requests. There are two prominent techniques employed for reducing the response latency: keep fully initialized containers alive (Warm Container) or reduce the new container startup (cold start) latency. This paper presents the 3rd container startup mode: Hibernate Container, which starts faster than the cold start container mode and consumes less memory than the Warm Container mode. Hibernate Container is essentially a "deflated" Warm Container. Its application memory is swapped out to disk, the freed memory is reclaimed and file based mmap memory is cleaned-up. The Hibernate Container's deflated memory is inflated in response to user requests. As Hibernate Container's application is fully initialized, its response latency is less than the cold start mode; and as the application memory is deflated, its memory consumption is less than the Warm Container mode. Additionally, when a Hibernate Container is "woken up" to process a request, the Woken-up Container has similar response latency to Warm Container but less memory consumption because not all the deflated memory needs to be inflated. We implemented the Hibernate technique as part of the open source Quark secure container runtime project and our test demonstrated that Hibernate Container consumes about 7\% to 25\% of the Warm Container memory. All of this results in a higher deployment density, lower latency and appreciable improvements in the overall system performance.