Exhausters and coexhausters were proposed by V.F. Demyanov and is used for studying nonsmooth functions. These objects are families of convex compact sets in terms of which optimality conditions are described. This makes possible to construct effective optimization algorithms for nonsmooth problems. Exhausters and coexhausters are not uniquely defined. The smaller families the easier computations. So the problem of finding the minimal family arises. V.A. Roshchina was the first who considered this problem for exhausters. Here we consider the same problem for coexhausters. We use Roshchina's definition of minimality but propose another, more geometric approach to this question.