A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A one-point solution for TU-games assigns a payoff distribution to every TU-game. In this paper we discuss a class of solutions containing all convex combinations of the CIS-value, the ENSC-value, and the egalitarian solution. We characterize this class of solutions using a general standardness for two player games and reduced game consistency. Specific cases of these properties characterize specific solutions in this class.