We present measurements of the tt-bar production cross section in
b-tagged lepton + jets events from p anti-p collisions at 1.96 TeV using the
CDF detector at Fermilab.  B-jets are tagged with either a secondary vertex
algorithm, or a soft lepton tagger that identifies muons from B hadron
semileptonic decays.  With Tevatron Run II data, we estimate the tt-bar
signal fraction in two different ways: by estimating the various background
contributions, and by fitting directly the leading jet transverse energy
spectrum for the signal and background contributions.  A subset of the
sample, with two secondary vertex tagged jets, yields a production cross
section consistent with the inclusive measurements.  Results are consistent
with a Standard Model tt-bar signal and current measurements of the top
quark mass.