The singleton and doubleton minors of a polymatroid encode a surprising amount of information about its structural complexity. Starting with a k-polymatroid ρ, we subtract from it as many maximally-separated matroids as possible. Let the result be an m-polymatroid; this gives rise to a notion of boundedness for ρ. When k is sufficiently large, the bounds on the singleton and doubleton minors of ρ completely determine the bound on ρ. Much of this is motivated and guided by the polytopal perspective of polymatroids. Our results provide an organized framework for thinking about polymatroid excluded minor problems.