Aims. We consider the influence of viscous dissipation on “spine” reconnection solutions in coronal plasmas. It is known from 2D and 3D “fan” reconnection studies that viscous losses can be important. We extend these arguments to 3D “spine” reconnection solutions. Methods. Steady 3D spine reconnection models were constructed by time relaxation of the governing visco-resistive MHD equations. Scaling laws were derived that compare the relative importance of viscous and resistive damping. Results. It is shown that viscous dissipation in spine reconnection models can dominate resistive damping by many orders of magnitude. A similar conclusion, but with less severe implications, applies to current sheet “fan” solutions. These findings are not sensitive to whether classical or Braginskii viscosity is employed.