The synthesis of ethylene vinyl halide (EVH) copolymers containing fluorine, chlorine, and bromine via the ADMET copolymerization of halogen containing alpha-omega-dienes with 1,9-decadiene is presented. The statistically random nature of the copolymers was established from their C-13 NMR spectra. Thermal analysis via differential scanning calorimetry points to a distinct difference in the crystallization behavior of these random copolymers when compared to, their compositionally matched precise analogues. In this case, sharp melting peaks typical of homopolymer-like crystallization of the precise analogues are no longer observed in Cl- and Br-based random copolymers and are replaced by broader peaks indicating a mechanism based on the selection of long crystallizable sequences. The results presented herein thus point to the utility of these random ADMET copolymers as suitable models for industrially relevant PE copolymers based on the perfectly linear, defect-free, and statistically random copolymer composition.