Summary: We understand a solution of a cooperative TU-game as the \(\alpha\)-prenucleoli set, \(\alpha\in R\), which is a generalization of the notion of the \([0, 1]\)-prenucleolus. We show that the set of all \(\alpha\)-nucleoli takes into account the constructive power with the weight \(\alpha\) and the blocking power with the weight \((1-\alpha)\) for all possible values of the parameter \(\alpha\). The further generalization of the solution by introducing two independent parameters makes no sense. We prove that the set of all \(\alpha\)-prenucleoli satisfies properties of duality and independence with respect to the excess arrangement. For the considered solution we extend the covariance propertywith respect to strategically equivalent transformations.