[en] A multichannel K-matrix formalism which accounts for the effect of inelastic thresholds is used to study the J/sup P/ = 3^- and 2⁺ dibaryon systems. An analysis, carried out previously for the J/sup P/ = 2⁺ system, is presented for the J/sup P/ = 3^- system. The relationship between phase-shift behavior and background contributions to the scattering matrix is then probed by studying both J/sup P/ systems using explicit K-matrix poles. Possible effects of the rd channel are considered and a three-channel analysis is performed for the J/sup P/ = 2⁺ system. The analyses are consistent with the existence of a J/sup P/ = 3^- and a J/sup P/ = 2⁺ dibaryon resonance