  We prove existence and a.e. regularity of an area minimizing soap film with a
bound on energy spanning a given Jordan curve in R^3. The energy of a film is
defined to be the sum of its surface area and the length of its singular
branched set. The class of surfaces over which area is minimized includes
images of disks, integral currents, nonorientable surfaces and soap films as
observed by Plateau with a bound on energy. Our area minimizing solution is
shown to be a smooth surface away from its branched set which is a union of
Lipschitz Jordan curves of finite total length.
