We present three measurements of the top-quark mass in the lepton plus jets channel with approximately 1.9  fb−1 of integrated luminosity collected with the CDF II detector using quantities with minimal dependence on the jet energy scale. One measurement exploits the transverse decay length of b-tagged jets to determine a top-quark mass of 166.9+9.5−8.5(stat)±2.9(syst)  GeV/c2, and another the transverse momentum of electrons and muons from W-boson decays to determine a top-quark mass of 173.5+8.8−8.9(stat)±3.8(syst)  GeV/c2. These quantities are combined in a third, simultaneous mass measurement to determine a top-quark mass of 170.7±6.3(stat)±2.6(syst)  GeV/c2.