Non-crosslinked polyolefin films or doped crosslinked polyolefin films (i.e., crosslinked polyolefin films that include a tear-alignment additive) may be used to shrink-wrap packages to create a wrapped package that is protected from tampering and damage but is also easy to open with little effort required by the customer. There is no need for perforations, and the films are quiet when torn, folded, cut, etc. Tear initiating cuts may be formed in the film. A tab may be placed over the film, and when the tab is pulled it applies enough force to start a pair of straight tears. The tears may be parallel or perpendicular to each other. The tears propagate in non-crosslinked polyolefin easily in the machine direction of the film as the tab continues to be pulled. In a doped crosslinked polyolefin, the tears propagate in the machine direction or perpendicular to the machine direction of the film.