In his classic article "An Essay on Bargaining" Schelling (1956) argues that ignorance might actually be strength rather than weakness. We test and confirm Schelling's conjecture in a simple take-it-or-leave bargaining experiment where the proposer can choose between two possible offers. Option A always gives the proposer a higher payoff than option B. The payoff of the responder depends on the (randomly determined) state of nature, i.e., in state s2 payoffs of the two players are aligned while they are not in state s1. The responder is always informed about the actual state. The proposer knows the actual state in our first treatment but not in the second. We find that proposers indeed benefit from ignorance because the responders accept almost all offers (even the unfavorable ones) if the payoffs of the responder have not been transparent for the proposer. In additional treatments we investigate situations where the proposer can deliberately remain ignorant. One could assume that remaining ignorant on purpose would be punished by the responder at least if an unfavorable outcome results. Surprisingly, we find that strategically remaining ignorant tends to be beneficial for the proposer particularly if the responder does not know with certainty whether it was the proposer's intention to remain ignorant or whether it was not her intention.