Processes are disclosed for oxygen-tailoring polyethylene, particularly polyethylenes suitable for wire and cable applications. One process includes conveying a first polyethylene having a melt index ≦5.0 and an MWD ≦5.0 through mixing or extrusion apparatus having a feed zone, a melt-mixing zone downstream of the feed zone, and a melt zone downstream of the melt-mixing zone, wherein the temperature of the first polyethylene in the melt zone ranges from about 180° C. to about 300° C.; and contacting the first polyethylene with an amount of an oxygen-containing gas having at least about 20.0 parts by weight oxygen per million per parts by weight of the first polyethylene (ppm (wt) O2). Polyethylene compositions having improved properties, particularly for wire and cable applications are disclosed.