Two new filtering/diffusion operators have been implemented in the Community Atmosphere Model finite-volume dynamical core (CAM-FV). First, a fourth-order divergence damping operator has been added to optionally replace the second-order version that has traditionally been used. This provides more scale selective dissipation of divergent modes that can generate grid-scale noise in CAM-FV if not damped properly. For example, data assimilation runs using CAM-FV DART (Data Assimilation Research Testbed) have revealed potential noise problems at the grid scale that can be alleviated significantly using higher-order divergence damping. Second, a ‘Laplacian’-type damping operator has been implemented to increase the explicit momentum dissipation in the top-of-atmosphere sponge layers. This helps control the excessive polar night jets that have been observed in ultra-high-resolution CAM-FV simulations. Results from stand-alone CAM-FV and CAM-FV DART are presented in this paper along with details on the implementation of the new operators.