This invention relates to high density polyethylene blown films having good barrier properties and improved processing characteristics. The method incorporates the use of peroxide which results in improved bubble stability without sacrifice in barrier properties. The polyethylenes have a density greater than about 0.950 g/cc, are relatively narrow in molecular weight distribution MWD (in the range of from about 2.0 to about 6.5), and are of medium molecular weight. In an embodiment, the films also have a rheological breadth parameter, a, that has been reduced by at least about 5%, but not more than 45%, by addition of a peroxide to the polyethylene. The addition of peroxide improves processability without sacrificing strength and barrier properties such as oxygen transmission rate.