We describe measurements of the quality factors of resonances in fibers made of tungsten, silicon, sapphire, and fused quartz. The silicon and sapphire samples exhibited losses consistent with thermoelastic damping. Our fused quartz samples showed excess loss at some frequencies. The tungsten fibers had quality factors much lower than the thermoelastic prediction at all frequencies that we measured. We calculate the expected Brownian motion of pendulums made with similar fibers.