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 17