Summary: The search for gravitational wave signals from astrophysical sources has led to the current work to upgrade the two largest of the long-baseline laser interferometers, the LIGO detectors. The first fused silica mirror suspensions for the Advanced LIGO gravitational wave detectors have been installed at the LIGO Hanford and Livingston sites. These quadruple pendulums use synthetic fused silica fibers produced using a \(\mathrm{CO}_{2}\) laser pulling machine to reduce thermal noise in the final suspension stage. The suspension thermal noise in Advanced LIGO is predicted to be limited by internal damping in the surface layer of the fibers, damping in the weld regions, and the strength of the fibers. We present here a new method for increasing the fracture strength of fused silica fibers by laser polishing of the stock material from which they are produced. We also show measurements of mechanical loss in laser polished fibers, showing a reduction of 30% in internal damping in the surface layer.