This study is aimed at determining the effect of the minute liquid compressibility on the flow of ink in a piezo-diaphragm driven Drop-On-Demand (DOD) ink jet nozzle. This goal is achieved by a comparison between the results obtained numerically for compressible and incompressible flows by means of Computational Fluid Dynamics calculations. In these calculations the exact geometry of the entire flow channel is modeled. Significant differences between the two flow models are observed in many aspects of the flow and drop evolution characteristics. Also, in some cases, seemingly similar features have been found to result from different physical driving forces. Despite the low Mach number and low condensation values involved, the very slightly compressible flow and the incompressible flow are very different. It is concluded that acoustic effects cannot be ignored and the incorporation of ink compressibility in the physical analysis of this flow system is essential.