Application containers, such as Docker containers, are light-weight virtualization environments that "contain" applications together with their resources and confguration information. While they are becoming increasingly popular as a method for agile software deployment, current techniques for preparing containers add unnecessary bloat into them: they often include unneeded fles that increase the container size by several orders of magnitude. This not only leads to storage and network transfer issues but also security concerns. The problem is well-recognized but available solutions are mostly ad-hoc and not largely deployed. Our previous work, Cimplifier, on debloating containers uses dynamic analysis to identify the resources necessary to a container and then debloat it. However, the dynamic analysis uses model executions or test runs, which if incomplete, may not allow detection of all the necessary resources. Therefore, it is important to explore other directions towards container debloating. In this paper, we discuss two of them: a new intermediate representation allowing incorporation of multiple techniques, such as dynamic analysis and static analysis, for debloating; and test case augmentation using symbolic execution.