Abstract: 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(-8.5)(+9.5)(stat) +/- 2.9(syst) GeV/c(2), and another the transverse momentum of electrons and muons from W-boson decays to determine a top-quark mass of 173.5(-8.9)(+8.8)(stat) +/- 3.8(syst) GeV/c(2). 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/c(2) .