The mechanical quality factor of a carbon dioxide laser-welded fiber was measured and compared to flame-welded fibers to determine the suitability of laser welding for attaching suspension fibers to test masses in precision experiments. The loss in the fiber was found to be limited primarily by thermoelastic damping and surface loss, rather than loss from the weld. This technique is attractive for the attachment of fused silica suspensions where low thermal noise and precision location of the weld are considered.