We propose a cooperative solution concept for general extensive games that can improve upon subgame-perfect Nash equilibrium. This new concept, which we label the subgame-perfect core, is a refinement of the core of the extensive game in the same sense as the set of subgame-perfect Nash equilibria is a refinement of the set of Nash equilibria. From its definition and properties, our concept is a cooperative analog of the non-cooperative subgame-perfect Nash equilibrium. Moreover, the subgame-perfect core has “perfection” properties; each subgame-perfect core payoff vector can be obtained as a subgame-perfect Nash equilibrium payoff vector of a modified extensive game that differs from the original game only in terms of the distribution of players’ payoffs at a terminal node. In this paper, we restrict ourselves to extensive games of perfect information with transferable utility. Consequently, each decision node determines a subgame, and terminal payoffs can be added and distributed among the players in the game.