We report a measurement of the tt-bar production cross section
using dilepton events with jets and missing transverse energy in p anti-p
collisions at s**(1/2) = 1.96 TeV.  Using 197 pb-1 of data recorded by the
upgraded Collider Detector at Fermilab (CDF II), we use two complementary
techniques to select candidate events.  The combined result yields a tt-bar
production cross section of 7.0+2.4_-2.1(stat)+1.6_-1.1(syst) +/- 0.4
(luminosity) pb which is consistent with the Standard Model.