A search for new dielectron-mass resonances using data recorded by the CDF II detector and corresponding to an integrated luminosity of 5.7  fb−1 is presented. No significant excess over the expected standard model prediction is observed. In this data set, an event with the highest dielectron mass ever observed (960  GeV/c2) was recorded. The results are interpreted in the Randall-Sundrum (RS) model. Combined with the 5.4  fb−1 diphoton analysis, the RS-graviton lower-mass limit for the coupling k/MPl=0.1 is 1058  GeV/c2, making it the strongest limit to date.