Structural VAR models are frequently identified using sign restrictions on impulse responses. Moving beyond the popular but restrictive Normal-inverse-Wishart-Uniform prior, we develop a methodology that can handle almost any prior distribution on contemporaneous responses. We then propose a new sampler that explores the posterior just as efficiently as done by the existing algorithm for the Normal-inverse-Wishart-Uniform case. We use this exible and tractable framework to combine sign restrictions with information on the volatility of the data, giving less prior mass to impulse effects that are inconsistent with the data from a training sample. This approach sharpens posterior bands and makes sign restrictions more informative. We apply the methodology to the oil market and show that oil supply shocks have a non-negligible effect on oil price dynamics.