When does restricting your opponent's freedom hurt you?

I examine the payoff consequences for a player when she removes a subset of her opponent's actions before playing a two-player complete information normal form game. When she faces a constraint on the maximal number of actions she can remove, she can be strictly better off by not removing any actions. I present such an example. I also establish sufficient conditions under which removing opponent's actions cannot hurt. As a corollary, I also characterize a necessary condition for a player's optimal Nash Equilibrium in games with generic payoffs when her opponent has strictly more actions than she does.