Approximate P-wave dispersion relations for K-N scattering are considered, under the assumption that the KΛN and KΣN interactions are of the odd intrinsic-parity, Yukawa type. If the crossing terms (which involve the P-wave K̄-N amplitudes) are neglected, the predictions of the equations are contradicted by the experimental evidence. However, the presence of virtual pion-hyperon states may enhance the K̄-N amplitudes sufficiently that they play an important role in the equations. It is shown that if the isotopic spin 1, P32 K̄-N absorptive amplitude is particularly strong, the contradiction with experiment may be removed. The possibility of even-parity K-baryon reactions is discussed briefly.