Grushko's theorem [Mat. Sb. 8 (1940) 169-182] says that any generating tuple (g 1 , . . . , gm) of a free product H * K is Nielsen-equivalent to a tuple (h 1 , . . . , h l , k l+1 , . . . , km) with h i ∈ H and k i ∈ K for all i. The h i and k i are clearly not unique. In this paper we address the extent of this non-uniqueness.