Abstract: A measurement of the top-quark pair-production cross section in p (p) over bar collisions at root s = 1.96 TeV using data corresponding to an integrated luminosity of 1.12 fb(-1) collected with the Collider Detector at Fermilab is presented. Decays of top-quark pairs into the final states ev + jets and μv+ jets are selected, and the cross section and the b-jet identification efficiency are determined using a new measurement technique which requires agreement between the measured cross sections with exactly one and with multiple identified b quarks from the top-quark decays. Assuming a top-quark mass of 175 GeV/c(2), a cross section of 8.5 +/- 0.6(stat) +/- 0.7(syst)pb is measured.