We calculate excess noise factors (Petermann K-factors) for a circular confocal unstable resonator. Typical mode profiles, and the dependence of their eigenvalues and K-factors on cavity geometry, are presented. The calculations are based upon the 'virtual source' method as well as on a self-consistent solution of the Huygens-Fresnel integral equation. It is known that in a one-dimensional strip resonator, K-factors ~104 are possible; although simple arguments suggest that the K-factors in two dimensions should vary roughly as the square of their one-dimensional counterparts, this turns out to occur only in rectangular symmetry and not in the circular case.
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