Information abstraction is one of the methods for tackling large extensive-form games (EFGs). Removing some information available to players reduces the memory required for computing and storing strategies. We present novel domain-independent abstraction methods for creating very coarse abstractions of EFGs that still compute strategies that are (near) optimal in the original game. First, the methods start with an arbitrary abstraction of the original game (domain-specific or the coarsest possible). Next, they iteratively detect which information is required in the abstract game so that a (near) optimal strategy in the original game can be found and include this information into the abstract game. Moreover, the methods are able to exploit imperfect-recall abstractions where players can even forget the history of their own actions. We present two algorithms that follow these steps -- FPIRA, based on fictitious play, and CFR+IRA, based on counterfactual regret minimization. The experimental evaluation confirms that our methods can closely approximate Nash equilibrium of large games using abstraction with only 0.9% of information sets of the original game.