This paper reports a measurement of the cross section for the pair production of top quarks in pp collisions at s√=1.96  TeV at the Fermilab Tevatron. The data were collected from the CDF run II detector in a set of runs with a total integrated luminosity of 1.1  fb−1. The cross section is measured in the dilepton channel, the subset of tt events in which both top quarks decay through t→Wb→ℓνb, where ℓ=e, μ, or τ. The lepton pair is reconstructed as one identified electron or muon and one isolated track. The use of an isolated track to identify the second lepton increases the tt acceptance, particularly for the case in which one W decays as W→τν. The purity of the sample may be further improved at the cost of a reduction in the number of signal events, by requiring an identified b jet. We present the results of measurements performed with and without the request of an identified b jet. The former is the first published CDF result for which a b-jet requirement is added to the dilepton selection. In the CDF data there are 129 pretag lepton+track candidate events, of which 69 are tagged. With the tagging information, the sample is divided into tagged and untagged subsamples, and a combined cross section is calculated by maximizing a likelihood. The result is σtt=9.6±1.2(stat)+0.6−0.5(sys)±0.6(lum)  pb, assuming a branching ratio of BR(W→ℓν)=10.8% and a top mass of mt=175  GeV/c2.