We present spectroscopic measurements of seven vibrational levels nu = 29-35 of the A(1(1)Sigma(+)(u)) excited state of Li-2 molecules by the photoassociation of a degenerate Fermi gas of Li-6 atoms. The absolute uncertainty of our measurements is +/- 0.000 02 cm(-1) (+/- 600 kHz) and we use these new data to further refine an analytic potential for this state. This work provides high accuracy photoassociation resonance locations essential for the eventual high-resolution mapping of the X(1(1)Sigma(+)(g)) state enabling further improvements to the s-wave scattering length determination of Li and enabling the eventual creation of ultracold ground- state Li-6(2) molecules.