The core's standard definition allows a blocking coalition to divide its joint payoff in whatever way the challenged allocation makes convenient, so that a coalition may threaten with different agreements against different proposals. We require instead that a coalition's threat be unconditional: the outcome it expects from the subgame it would play on its own. The consequences are economic as much as technical. We exhibit agreements in which a player who contributes nothing to any coalition is nevertheless paid, and in which players who would otherwise compete for a partner gain by declining to compete, neither being any longer undercut by an agreement tailored to the deal on the table. The resulting solution, the ut-core, contains the core, and in cases of the above kind is non-empty where the core is silent. The construction turns any solution concept for the subgames into another one for the game itself, the ut-core being the image of the core; the solution that reproduces itself under the operation is its recursive counterpart, not nested with it in either direction. We characterize the solution for three-player games, and also establish non-emptiness for symmetric superadditive games.