We study the |Delta I|=3/2 amplitudes of the octet-hyperon decays B -> B' + pion and of the decays Omega^- -> Cascade + pion in the context of heavy-baryon chiral perturbation theory. For the octet-hyperon decays, we investigate the theoretical uncertainty of the lowest-order predictions by calculating the leading non-analytic corrections. We find that these corrections are within the expectations of naive power counting and, therefore, that this picture can be tested more accurately with improved measurements. For the Omega- decays, we obtain at leading order two operators responsible for the decays which also contribute at one loop to the octet-hyperon decays. These one-loop contributions are sufficiently large to suggest that the ratio of measured widths of Omega^- -> Cascade0 + pion- to Omega^- -> Cascade- + pion0 being approximately equal to 2.7 may be too large.