  We present a measurement of the isolated direct photon cross section in
p-pbar collisions at sqrt(s) = 1.8 TeV and |eta| < 0.9 using data collected
between 1994 and 1995 by the Collider Detector at Fermilab (CDF). The
measurement is based on events where the photon converts into an
electron-positron pair in the material of the inner detector, resulting in a
two-track event signature. To remove pi0 -> gamma gamma and eta -> gamma gamma
events we use a new background subtraction technique which takes advantage of
the tracking information available in a photon conversion event. We find that
the shape of the cross section as a function of pT is poorly described by
next-to-leading-order QCD predictions, but agrees with previous CDF
measurements.
