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 tt¯ events in the lepton+jets final state. One method uses an event-based likelihood technique resulting in Mtop=173.2+2.6−2.4(stat)±3.2(syst)  GeV/c2 or 173.2+4.1−4.0  GeV/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 for Mtop of 173.5+3.7−3.6(stat)±1.3(syst)  GeV/c2 or 173.5+3.9−3.8  GeV/c2. We take the latter, which is more precise, as our result.