We present a measurement of the top quark mass with tt dilepton events produced in pp 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 tt candidates. To account for the unconstrained event kinematics, we scan over the phase space of the azimuthal angles (ϕν1,ϕν2) of neutrinos and reconstruct the top quark mass for each ϕν1, ϕν2 pair by minimizing a χ2 function in the tt 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 tt and background events, and parametrized in order to provide continuous probability density functions. A likelihood fit to the mass distribution in data as a weighted sum of signal and background probability density functions gives a top quark mass of 165.5+3.4−3.3(stat)±3.1(syst)  GeV/c2.