Structural VAR models are frequently identified using sign restrictions on contemporaneous impulse responses. We develop a methodology that can handle a set of prior distributions that is much larger than the one currently allowed for by traditional methods. We then develop an importance sampler that explores the posterior distribution just as conveniently as with traditional approaches. This makes the existing trade-off between careful prior selection and tractable posterior sampling disappear. We use this framework to combine sign restrictions with information on the volatility of the variables in the model, and show that this sharpens posterior inference. Applying the methodology to the oil market, we find that supply shocks have a strong role in driving the dynamics of the price of oil and in explaining the drop in oil production during the Gulf war.