We develop an importance sampler for sign restricted Bayesian structural vector autoregressive models. The algorithm nests as a special case the sampler associated with the popular Normal inverse Wishart Uniform prior, while allowing to move beyond such prior in medium sized models. We then propose a prior on contemporaneous impulse responses that provides flexibility on the magnitude and shape of the impact responses. We illustrate the quantitative relevance of the choice of the prior in an application to US monetary policy shocks. We find that the real effects of monetary policy shocks are stronger under our proposed prior than in the Normal inverse Wishart Uniform setup.