Using narrow-bandwidth vacuum-ultraviolet radiation generated by difference-frequency four-wave mixing in Xe, the O-2 photoabsorption cross section in the Schumann-Runge system B (3)Sigma (-)(u)<--X (3)Sigma (-)(g), near the dissociation limit of the B state, is measured with a resolution of similar to0.1 cm(-1) full-width at half-maximum. The rotational structure of B-X(22,0) is assigned for the first time, and evidence is found for transitions into the F-1 levels of B(v=23). Experimental values for the triplet-splitting constants lambda and gamma for B(v=22) are found to be inconsistent with the rising trend observed for v less than or equal to 19, due to a change in the sense of the perturbation of the B-state levels by the C-' (3)Pi (u) levels near B(v=20). A new value for the dissociation energy of the B state, D(B)=57 136.2 +/-0.3 cm(-1), determined from an analysis of the observed and missing lines near the dissociation limit, is in excellent agreement with previous values arising from the observation of rotational thresholds in the Schumann-Runge continuum.