Unlike perfect-information games, imperfect-information games cannot be solved by decomposing the game into subgames that are solved independently. Thus more computationally intensive equilibrium-finding techniques are used, and all decisions must consider the strategy of the game as a whole. While it is not possible to solve an imperfect-information game exactly through decomposition, it is possible to approximate solutions, or improve existing solutions, by solving disjoint subgames. This process is referred to as subgame solving. We introduce subgame solving techniques that outperform prior methods both in theory and practice. We also show how to adapt them, and past subgame-solving techniques, to respond to opponent actions that are outside the original action abstraction; this significantly outperforms the prior state-of-the-art approach, action translation. Finally, we show that subgame solving can be repeated as the game progresses down the tree, leading to significantly lower exploitability. We applied these techniques to develop the first AI to defeat top humans in heads-up no-limit Texas hold'em poker.