High-quality positron lifetime measurements (70 million total counts) are reported for polyethylenes (PEs) of different crystallinities (X-c = 3-82%). The specific volumes of the crystalline and amorphous phases (V-c and V-a, respectively) were estimated from density and wide-angle X-ray scattering (WAXS) experiments. Some samples (those with low values of X-c) were branched PEs, and those with high values of X-c were linear PEs for which X-c was varied with changes in the crystallization temperature. Both V-c and V-a increase with decreasing X-c in the range 0% less than or equal to X-c less than or equal to 56% (the branched PEs) but are constant for X-c : 56% (the linear PEs). The lifetime spectra were analyzed with the MELT and LIFSPECFIT routines. Artifacts that can appear in the spectrum analysis were checked via an analysis of computer-generated spectra. Four lifetime components appeared in all of the PEs; the two long-lived ones are attributed to pick-off annihilation of ortho-positronium (o-Ps) in crystalline regions (tau (3)) and in holes of the amorphous phase (tau (4)). With increasing X-c, tau (3) decreases from about 1.2 to 1 ns, tau (4) decreases from 3.0 to 2.5 ns, and the intensity I-4 decreases from 29 to 0%. An increase in I-3 from 6 to 12% was observed. A comparison with simulations shows that the true I-3 value approaches 0 for X-c --> 0%. The decrease in I-4 is weaker than the increase in X-c; this leads to the conclusion that the apparent specific o-Ps yield in the amorphous phase I-4(Xc) increases with X-c. Possible reasons for this surprising results are discussed. The fractional free hole volume [h = (V-a - V-occ)/V-a, where V-occ is the crystalline occupied volume] was estimated from density and WAXS results. Between X-c = 0 and 56%, h decreases from 0.151 to 0.090, but it does not change further above X-c = 56%. The mean size (v) of the local free volumes (holes) estimated from tau (4) decreases from 200 to 150 Angstrom (3). The number density of holes (Nh) calculated from these values (N-h = h/v) also decreases from 0.8 to 0.6 nm(-3) in the range 0% less than or equal to X-c less than or equal to 56%. The values of V-a, V-c, h, and N-h increase with an increasing degree of branching but do not vary for linear PEs. The possible influence of a crystalline-amorphous interfacial phase (three-phase model) on the observed lifetime parameters is also discussed.