We present results of a search in 929 +/- 56 pb-1 of p anti-p
collisions at 1.96 TeV for the anomalous production of events containing a
charged lepton (l, either e or mu) and a photon, both with high transverse
momentum, accompanied by additional signatures, X, including missing
transverse energy (E/_T) and additional leptons and photons. We use the
same selection criteria as in the previous CDF Run I search, but with an
order-magnitude larger data set, a higher p anti-p collision energy, and the
CDF II detector.