  On a Fano manifold M we study the supremum of the possible t such that there
is a K\"ahler metric in c_1(M) with Ricci curvature bounded below by t. This is
shown to be the same as the maximum existence time of Aubin's continuity path
for finding K\"ahler-Einstein metrics. We show that on P^2 blown up in one
point this supremum is 6/7, and we give upper bounds for other manifolds.
