Using laser-induced fluorescence techniques applied to Schumann-Runge absorption transitions from vibrationally excited O2(X3SIGMA(g)-), we have measured the rotational and fine-structure level-specific linewidths in v=0 and v=2 of the B3SIGMA(u)- state. These linewidths represent the first measurement of fine-structure level-specific predissociation rates in B2SIGMA(u)-(v<10), and they are found to vary considerably among the various rotational and fine-structure levels, encompassing a range of 0.09-0.34 cm-1 in v=0, N' less-than-or-equal-to 36, and 0.4-1.4 cm-1 in v=2, N' less-than-or-equal-to 24. Orbit-rotational coupling in the B3SIGMA(u)--3PI(u) interaction, in addition to spin-orbit coupling in the B3SIGMA(u)--1PI(u), - 3PI(u), - 5PI(u) interactions, is found to be crucial to explaining the relative predissociation rates among the fine-structure levels, even in low rotational levels. Measurements were made in the (v',v'') = (0,9), (0,10), (0,21), (2, 10), and (2,22) Schumann-Runge [B3SIGMA(u)-(v') <-- X3SIGMA(g)-(v'')] bands without presumption as to the molecular constants in either the X or B states. The use of high ground state vibrational levels as a starting point for the photoexcitation measurements produces a spectral separation among the previously blended triplet components of the absorption lines. All lines in these bands are found to be broadened by predissociation, with those terminating in v'=0 and in the N'=J'-1 (F'1) levels exhibiting the smallest effect.