Submitted to Phys. Rev. DWe present a measurement of the top quark mass with t-tbar dilepton events produced in p-pbar collisions at the Fermilab Tevatron (s=1.96 TeV) and collected by the CDF II detector. A sample of 328 events with a charged electron or muon and an isolated track, corresponding to an integrated luminosity of 2.9 fb−1, are selected as t-tbar candidates. To account for the unconstrained event kinematics, we scan over the phase space for the azimuthal angles (ϕν1,ϕν2) of neutrinos and reconstruct the top quark mass by minimizing a χ2 function in the t-tbar dilepton hypothesis. We assign χ2-dependent weights to the solutions in order to build a preferred mass for each event. Preferred mass distributions (templates) are built from simulated t-tbar and background events, and parameterized in order to provide continuous probability density functions. A likelihood fit of the preferred mass distribution in data to a weighted sum of signal and background probability density functions gives a top quark mass of 165.5−3.3+3.4(stat.)±3.1(syst.) GeV/c2