We present results of a search at CDF in 929±56  pb−1 of pp collisions at 1.96 TeV for the anomalous production of events containing a high-transverse momentum charged lepton (ℓ, either e or μ) and photon (γ), accompanied by missing transverse energy (E̸T), and/or additional leptons and photons, and jets (X). We use the same selection criteria as in a previous CDF Run I search, but with an order-magnitude larger data set, a higher pp collision energy, and the CDF II detector. We find 163 ℓγE̸T+X events, compared to an expectation of 150.6±13.0 events. We observe 74 ℓℓγ+X events, compared to an expectation of 65.1±7.7 events. We find no events similar to the Run I eeγγE̸T event.