  In joint work with Chen and Weber, the author has elsewhere shown that
CP2#2(-CP2) admits an Einstein metric. The present paper gives a new and rather
different proof of this fact. Our results include new existence theorems for
extremal Kahler metrics, and these allow one to prove the above existence
statement by deforming the Kahler-Einstein metric on CP2#3(-CP2) until
bubbling-off occurs.
