  Thermal noise of optical reference cavities sets a fundamental limit to the
frequency instability of ultra-stable lasers. Using Levin's formulation of the
fluctuation-dissipation theorem we correct the analytical estimate for the
spacer contribution given by Numata et al.. For detailed analysis
finite-element calculations of the thermal noise focusing on the spacer
geometry, support structure and the usage of different materials have been
carried out. We find that the increased dissipation close to the contact area
between spacer and mirrors can contribute significantly to the thermal noise.
From an estimate of the support structure contribution we give guidelines for a
low-noise mounting of the cavity. For mixed-material cavities we show that the
thermal expansion can be compensated without deteriorating the thermal noise.
