Ultra-precision manufacturing (UPM) machines are used to fabricate and measure complex parts having micrometer-level features and nanometer-level tolerances/surface finishes. Therefore, random vibration of the machine due to ground excitations and residual vibration stemming from onboard disturbances must be mitigated using vibration isolation systems. A long-standing rule of thumb in vibration isolation system design is to locate the isolators in such a way that the vibration modes of the isolated machine are decoupled. However, prior work by the authors has demonstrated that coupling vibration modes of passively-isolated UPM machines could provide conditions for drastic reduction of residual vibrations compared to decoupling. The authors' analysis was based on the restrictive assumption that the isolated machine was modally damped. The key contribution of this paper is in investigating the effect of mode coupling on the residual vibrations of UPM machines with non-proportional (NP) damping which is more realistic than modal damping. It also analyzes the effects of mode coupling on the reduction of ground vibrations (i.e., transmissibility). The analyses reveal that, even though NP damping changes the vibration behavior of the machine compared to modal damping, mode coupling still provides ample opportunities to reduce residual vibration and transmissibility. Guidelines for properly designing a UPM machine to best exploit mode coupling for vibration reduction are provided and validated through simulations and experiments. Up to 40% reduction in residual vibration and 50% reduction in transmissibility are demonstrated. (C) 2015 Elsevier Inc. All rights reserved.