Boundary charges in gauge theories (like the ADM mass in general relativity) can be understood as integrals of linear conserved n-2 forms of the free theory obtained by linearization around the background. These forms are associated one-to-one to reducibility parameters of this background (like the time-like Killing vector of Minkowski space-time). For such n-2 forms, a non-linear completion is constructed that is closed in the full interacting theory and thus allows the use of Stokes theorem without bulk contributions, provided a one parameter solution to the full equations of motion with appropriate fall-off conditions is used and the reducibility parameters of the background are simultaneously reducibility parameters of this one parameter solution.