Motivated by our previous work using the Stillinger-Weber potential, which shows that the [<(2)over bar 11>] step on the relaxed 1 x 1 Si(111) has a Schwoebel barrier of 0.61+/-0.07 eV, we calculate here the same barrier corresponding to two types of kinks on this step-one with rebonding between upper and lower terrace atoms (type B) and the other without (type A). From the binding energy of an adatom, without additional relaxation of other atoms, we find that the Schwoebel barrier must be less than 0.39 eV (0.62 eV) for the kink of type A (type B). Such a bound is argued to be a robust feature following from the presence of rebonding at the step edge or kink site. From the true adatom binding energy we determine the Schwoebel barrier to be 0.15+/-0.07 eV (0.50+/-0.07 eV) for the kink of Type A (B). The decrease in the Schwoebel barrier is roughly consistent with our previous estimates of its upper bound of 0.05 eV. However, as the true binding energy plots show discontinuities due to significant movement of atoms at the kink site, we speculate on the possibility of multi-atom processes having smaller Schwoebel barriers.