Materials structurally equivalent to copolymers of ethylene and < 10 mol % of vinyl alcohol, vinyl acetate, methyl acrylate, tert-butyl acrylate, and acrylic acid were synthesized via ruthenium-catalyzed olefin metathesis copolymerization followed by polymer hydrogenation. These polymers differ from previous metathesis-derived linear polyethylene analogues in that they do not have precise sequence distributions, and therefore, they serve as superior models for chain-addition functional polyethylenes. The ester group-substituted polymers display rapid decreases in melting temperature and heat of fusion with increasing comonomer contents irrespective of the identity of the functional group, consistent with these groups being equally excluded from the crystal lattice. The alcohol-substituted polymers, however, show higher melting temperatures and a weaker property dependence on comonomer content as compared to the other polymers. Thus, the behavior of alkyl branch-free functionalized polyethylenes is consistent with the large body of work involving the effects of functional substituents on polyethylenes containing alkyl branches.