Lightweight integer compression algorithms play an important role in in-memory database systems to tackle the growing gap between processor speed and main memory bandwidth. Thus, there is a large number of algorithms to choose from, while different algorithms are tailored to different data characteristics. As we show in this paper, with the availability of byte-addressable non-volatile random-access memory (NVRAM), a novel type of main memory with specific characteristics increases the overall complexity in this domain. In particular, we provide a detailed evaluation of state-of-the-art lightweight integer compression schemes and database operations on NVRAM and compare it with DRAM. Furthermore, we reason about possible deployments of middle- and heavyweight approaches for better adaptation to NVRAM characteristics. Finally, we investigate a combined approach where both volatile and non-volatile memories are used in a cooperative fashion that is likely to be the case for hybrid and NVRAM-centric database systems.