As part of a more comprehensive investigation of following crystallization of polyethylene isobarically and isothermally at preselected portions of the pressure (P) and temperature (T) phase diagram within the P range of 2–5 kbar and supercoolings (ΔT) up to 10 °C, the present work is centered on formation, lateral growth (including measurement of growth rates), and melting of crystals. In the course of it the salient observation was made that, within the above specified P and ΔT range at least, all crystal growth occurs in the hexagonal phase, and only in this phase, irrespective of whether in the hexagonal (h) or orthorhombic (o) stability regime of the P-T phase diagram. In the latter case the h crystals represent a metastable form and transform into the stable o phase at some stage of growth, when, as now observed, all growth stops. The observed lower melting temperature of the h phase in the appropriate portion of the P-T phase diagram (“below” the triplet point) is consistent with all the above and introduces a newly recognized “nongrowth” region in the phase diagram. The lateral growth measurement of h crystal (the only crystals which are seen to grow) is readily interpretable by an activated growth mechanism when referred to the supercooling in the h form (as opposed to the o form, even when the latter is the stable one). Here the barrier attributable to nucleation is largely uneffected by P, but the preexponential (including transport) is retarded by increasing pressure. The implications of these findings for polymer crystallization are discussed, at this stage, in a provisional manner. © 1991, American Chemical Society. All rights reserved.