The viscous dissipation of axial field disturbances in planar magnetic X-points is examined. It is emphasized that an accurate treatment requires a nonisotropic tensor viscosity whose components are governed by the local magnetic field. Numerical solutions are constructed, which compare the buildup of viscous forces using the tensor formulation against a simplified model based on conventional shear viscosity. The scaling of the global energy-loss rate with the viscosity coefficient is shown to follow for both the traditional shear viscosity and the Braginskii bulk viscosity. This suggests that viscous wave dissipation can occur quite rapidly, in a few tens of Alfvén times. The results imply that large-scale disturbances, generated by magnetic reconnection in the solar corona, should dissipate in a time on the order of a few minutes and significantly contribute to coronal heating.