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Abstract: (joint work with Rosa Sena-Dias) A theorem of Derdziński from the 1980's establishes that certain Einstein metrics are conformal to Bach-flat extremal Kahler metrics. Using this result, Rosa Sena-Dias and I classified conformally Kähler, U(2)-invariant, Einstein metrics on the total space of O(−m). This yields infinitely many 1-parameter families of metrics exhibiting several different behaviors, including asymptotically hyperbolic, ALF, and metrics that compactify to a Hirzebruch surface with a cone singularity along the "divisor at infinity." As an application of these results, some interesting phenomena occur. For instance, we exhibit the Taub-bolt Ricci-flat ALF metric as a limit of cone angle Einstein metrics on the blow-up of CP² at a point (in the limit when the cone angle converges to zero). We also construct asymptotically hyperbolic Einstein metrics that are conformal to a scalar-flat Kähler metric and cannot be obtained by applying Derdziński's theorem.