We report measurements of the polarization of W bosons from top-quark decays using 2.7 fb^-1 of ppbar collisions collected by the CDF II detector. Assuming a top-quark mass of 175 GeV/c^2, three measurements are performed. A simultaneous measurement of the fraction of longitudinal (f_0) and right-handed (f_+) W bosons yields the model-independent results f_0 = 0.88 \pm 0.11 (stat) \pm 0.06 (syst) and f_+ = -0.15 \pm 0.07 (stat) \pm 0.06 (syst) with a correlation coefficient of -0.59. A measure