A reduction in the distortion of a single facet mirror, rotating at high speeds, was sought using finite element methods of analysis (FEA). Improvements in geometry were constrained by the need to preserve the original single facet shape, prescribed principal diameters and method of spindle mounting. The aim was to reduce the out-of-balance forces/moments and to simplify the method of balancing. The approach was to model the effects of the removal of surplus mass, in a simple manner to suit machine manufacturing, whilst maintaining the desired mirror inclination and aperture. Attention was paid to assessing the accuracy of the FEA method by employing purely analytical methods where possible. To this end, analytical solutions were derived and mathematical routines were written in MATLAB to provide the appropriate checks. In particular, the calculation of the moments of inertia about the principal axes and the modeling of the high stress regions at the location of the balance weights, were examined in detail. The given geometry was assembled from three parts, namely, a mirror cylinder, a balance ring and a clamping lock-nut. In order to take account of the relative compliance between these parts, it was necessary to model the system as an assembly of contacting surfaces with appropriate interference forces. It was found that the calculated distortions were excessively high and that satisfactory performance could only be met by fabricating the mirror from a single piece of material. Analysis of a single part mirror indicated that, with judicious removal of material, it was possible to balance the mirror in a single plane. This decreased the localized stress levels caused by the balancing weights and greatly reduced the distortion across the mirror surface.