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We propose a new solution concept for games in extensive form that incorporates both cooperation and subgame perfection. From its definition and properties, the new solution concept, named the subgame-perfect core, is a refinement of the core of an extensive game in the same sense as the set of subgame-perfect Nash equilibria is a refinement of the set of Nash equilibria. To further characterize the subgame-perfect core, we show that each subgame-perfect core payoff vector can be implemented as a non-cooperative solution, as it is a subgame-perfect Nash equilibrium payoff vector of an extensive form game that is closely related to the original game. We also motivate and introduce a related concept of subgame-perfect strong Nash equilibrium of an extensive game that is coalition proof.