Polyethylenes with Br, Cl, or F atoms placed at an equal distance of 21 or 15 backbone carbons are known to crystallize as homopolymers, accommodating the halogen in layered crystallites. In contrast, analogs with a random distribution display a crystallization path dominated by sequence-length selection. A consequence of the sequence selection of random copolymers is a constrained interlamellar region and broader melting peaks displaced at higher temperatures than analog systems with the precise placement. Precision and random ethylene-vinyl halides are excellent models to substantiate as a general behavior the strong melt-memory observed in random ethylene 1-alkene copolymers, which contrasts with a much weaker or lack of melt-memory seen in linear polyethylene. While precision polyethylenes with Br, Cl, or F placed on each 21st or 15th backbone carbon show negligible deviation in crystallization rate above the observed melting, the increase in crystallization rate of analogs with the random distribution is observed even from melts 60 degrees above the observed melting point. These data give further evidence of the sharp difference of melt-memory behavior between homopolymers and random copolymers, regardless of whether the co-unit participates in the crystalline regions. Differences in melt-annealing behavior, and a recrystallization of precision polyethylenes that depends on the polymorph that melts prior a subsequent cooling, are also highlighted.