  We present results of a search for anomalous production of events containing
a charged lepton (either electron or muon) and a photon, both with high
transverse momentum, accompanied by additional signatures, X, including missing
transverse energy (MET) and additional leptons and photons. We use the same
kinematic selection criteria as in a previous CDF search, but with a
substantially larger data set, 305 pb-1, a ppbar collision energy of 1.96 TeV,
and the upgraded CDF II detector. We find 42 Lepton+Photon+MET events versus a
standard model expectation of 37.3 +- 5.4 events. The level of excess observed
in Run I, 16 events with an expectation of 7.6 +- 0.7 events (corresponding to
a 2.7 sigma effect), is not supported by the new data. In the signature of
Multi-Lepton+Photon+X we observe 31 events versus an expectation of 23.0 +- 2.7
events. In this sample we find no events with an extra photon or MET and so
find no events like the one ee+gg+MET event observed in Run I.
