  We present a new method to measure the top quark pair production cross
section and the background rates with 2.7 fb$^{-1}$ of data from $p\bar{p}$
collisions at $\sqrt{s} =1.96$ TeV collected with the CDF II Detector. The size
of the dataset was chosen to directly show the improvements of this new method.
We select events with a single electron or muon, missing transverse energy, and
at least one b-tagged jet. We perform a simultaneous fit to a jet flavor
discriminant across nine samples defined by the number of jets and b-tags. We
measure a top cross section of $\sigma_{t\bar{t}} = 7.64 \pm 0.57 \mathrm{(stat
+ syst)} \pm 0.45 \mathrm{(luminosity)}$ pb. An advantage of this approach is
that many systematic uncertainties are measured in situ and inversely scale
with integrated luminosity.
