We report measurements of the polarization of W bosons from top-quark decays using 2.7 fb−1 of pp collisions collected by the CDF II detector. Assuming a top-quark mass of 175  GeV/c2, three measurements are performed. A simultaneous measurement of the fraction of longitudinal (f0) and right-handed (f+) W bosons yields the model-independent results f0=0.88±0.11(stat)±0.06(syst) and f+=−0.15±0.07(stat)±0.06(syst) with a correlation coefficient of −0.59. A measurement of f0 [f+] constraining f+ [f0] to its standard model value of 0.0 [0.7] yields f0=0.70±0.07(stat)±0.04(syst) [f+=−0.01±0.02(stat)±0.05(syst)]. All these results are consistent with standard model expectations. We achieve the single most precise measurements of f0 for both the model-independent and model-dependent determinations.