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We report two measurements of the top-quark mass Mtop using the CDF II detector at the Fermilab Tevatron in a 318 pb-1 data sample of tt̅ events in the lepton + jets final state. One method uses an event-based likelihood technique resulting inMtop = 173.2-2.4+2.6(stat) ± 3.2(syst) GeV/c2 or 173.2-4.0+4.1GeV/c2. The second method reconstructs a top-quark mass in each event using the measured invariant mass of the hadronically decaying W boson to constrain the jet energy scale to obtain a value forMtop of 173.5-3.6+3.7(stat) ± 1.3(syst) GeV/c2 or 173.5-3.8+3.9GeV/c2. We take the latter, which is more precise, as our result.