The large variety of plasma shapes produced in the TCV tokamak places unique demands on the plasma facing surfaces. In particular, the central column graphite armour tiles are solicited during the creation of all TCV plasmas and function as power handling surfaces for both limited and diverted discharges. The higher power flux densities accompanying the addition of electron cyclotron heating systems have necessitated a new, optimized, design for these tiles. The optimization process and the subsequent new tile design are described. A basic `two point' model of the scrape-off layer plasma in conjunction with TCV equilibrium reconstructions and a simplified representation of the local magnetic field line geometry are used to impose simulated power flux densities onto a parametric toroidal tile contour. The thermo-mechanical response of the tile is then investigated via full 3-D finite element simulations accounting for the non-linear temperature dependence of the graphite thermal diffusivity and radiation from the tile surface. The final design choice is a compromise between the requirements for adequate power handling for a range of magnetic configurations, the need to protect against tile edge misalignment in the presence of grazing field line angles of incidence and the space restrictions imposed by vacuum vessel design.