The extreme points of the set of contents (finitely additive measures) on an algebra \(\mathcal A\), which are majorized by a submodular set function \(u\), have already been characterized for certain special cases [see \textit{J. Rosenmüller}, Arch. Math. 22, 420-430 (1971; Zbl 0237.28002), \textit{F. Dalbaen}, J. Math. Anal. Appl. 45, 210-233 (1974; Zbl 0337.90084), \textit{D. Plachky}, Proc. Am. Math. Soc. 54, 193-196 (1976; Zbl 0285.28005)]. The main result of this paper gives a characterization for the case that \(u\) is a submodular set function of a particular simple form. On the way, a decomposition property of these contents is obtained using the Summensatz from \textit{H. König} [Arch. Math. 23, 500-508 (1972; Zbl 0248.46007)] and some results are proved for contents defined in terms of maximal filters.