The invention provides a process to form an ethylene-based polymer, said process comprising polymerizing ethylene in the presence of at least one free-radical agent, and in the presence of a "metal alkyl-containing compound" selected from the group consisting of the following: i) at least one "Group II metal alkyl-containing compound," ii) at least one "Group III metal alkyl-containing compound," or iii) a combination of i) and ii). The invention also provides a composition comprising at least one ethylene-based polymer, prepared from a free-radical polymerization, and wherein the ethylene-based polymer has the following property: y > 0.28567x - 0.00032, wherein y = vinyl/1000C, as determined by 1H NMR, and x = mol% polymerized ?-olefin, as determined by 13C NMR. The invention also provides a composition comprising at least one ethylene-based polymer, prepared from a free-radical polymerization, and wherein the ethylene-based polymer has the following properties: A) a vinyl content greater than, or equal to, 0.3 vinyl per 1000 C (total carbons), and B) a polymerized alpha-olefin level less than, or equal to, 1.00 mole percent, based on the total moles of polymerized monomers.