Summary: A strongly polynomial algorithm is developed for finding an integer-valued feasible \(st\)-flow of a given flow amount, which is decreasingly minimal on a specified subset \(F\) of edges in the sense that the largest flow value on \(F\) is as small as possible; within this, the second largest flow value on \(F\) is as small as possible; within this, the third largest flow value on \(F\) is as small as possible, and so on. A characterization of the set of these st-flows gives rise to an algorithm to compute a cheapest \(F\)-decreasingly minimal integer-valued feasible \(st\)-flow of given flow amount. Decreasing minimality is a possible formal way to capture the intuitive notion of fairness.