The technique of cavity ring-down (CRD) spectroscopy is particularly useful for measuring absorptions of very weak optical transitions. We have in this manner investigated the 40 950-41 300 cm(-1) region in O-2, where only absorption in the O-2(A (3) Sigma(u)(+)-X(3) Sigma(g)(-)) 11-0 band had been previously identified. Five new bands have been discovered in this range--the A’ (3) Delta(u)-X (3) Sigma(g)(-) 12-0 and 13-0 bands, the c (1) Sigma(u)(-)-X (3) Sigma(g-) 17-0 and 18-0 bands, and the A (3) Sigma(u)(+)-X (3) Sigma(g)(-) 12-0 band. The origins of the F-1 and F-2 components of the latter lie only 7 cm(-1) below the lowest dissociation limit, and 15 lines have been identified. No F-3 levels were observed; apparently all are above the dissociation limit. The high instrumental sensitivity of the CRD technique has allowed observation of weak lines of the A-X 11-0 band, and 12 of the 13 branches have been identified and their intensities measured. A very low upper limit has been set on the intensity of the thirteenth branch, Q(13). We find 107 unidentified lines in the region, the stronger ones (19) lying in the vicinity of lines of the A-X 11-0 band. The weaker ones (88) are spread throughout the spectral region, up to and even beyond the O-2 dissociation limit, and probably have their origin in transitions to very weakly bound O-2 states, which may have atmospheric significance. These weaker lines have intensities that are typically 1%-5% of the strong A-X 11-0 band lines.