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Graphene oxide (GO) films have a great potential for aerospace, electronics, and renewable energy applications due to their low cost and unique properties. For structural applications, they can achieve an exceptional combination of damping and stiffness. This study investigates the effect of packing density, reduction, and water removal on stiffness and damping of graphene oxide films. GO sheets dispersed in water are passed through a filter and deposited on a removable substrate. Through variations of the film fabrication process, films of both GO and reduced GO (rGO) are produced with varying levels of packing. Heat treatment is also used to remove the water in half of the films. The degree of packing is assessed through film density calculations. Microscopy as well as Raman and X-ray spectroscopy are used to measure the degree of packing while Dynamic Mechanical Analysis (DMA) is used to quantity mechanical damping and storage modulus of specimens in tension. Correlating mechanical properties to structure of films revealed new understanding of damping and stress transfer mechanisms in these materials. Optimal structures resulted in superior combinations of stiffness (18 GPa) and damping (0.14), potentially paving the way for using GO based films in advanced structural applications.