Context: Visco-resistive damping in line-tied magnetic X-points is examined. Aims: The goal is to determine whether fast, Alfvénic energy dissipation is possible for X-point disturbances damped by the plasma resistivity and non-isotropic viscosity. Methods: The response of X-points to planar and axial perturbations is explored numerically by solving the linearized compressible MHD equations in two and a half dimensions. Results: It is demonstrated that fast dissipation is possible in the case of non-reconnective planar disturbances damped by anisotropic viscosity in weakly resistive plasmas. Although perturbations which change the initial X-point topology decay slowly at large times when viscous effects are dominant, there is an initial phase in which a significant fraction of the disturbance energy is removed on an Alfvénic timescale. The decay of incompressive axial field disturbances occurs by a different mechanism, however, that is always formally slow (i.e. dependent on the small viscous and resistive damping coefficients). Conclusions: Computations suggest that fast, visco-resistive energy release in coronal plasmas is possible for compressive X-point disturbances. This result could have important implications for understanding rapid energy release in coronal active regions.