We propose algorithms for conducting Bayesian inference in structural vector autoregressions identified using sign restrictions. The key feature of our approach is a sampling step based on 'soft' sign restrictions. This step draws from a target density that smoothly penalises parameter values violating the restrictions, facilitating the use of computationally efficient Markov chain Monte Carlo sampling algorithms. An importance-sampling step yields draws from the desired distribution conditional on the 'hard' sign restrictions. Relative to standard accept-reject sampling, the method substantially improves computational efficiency when identification is 'tight'. It can also greatly reduce the computational burden of implementing prior-robust Bayesian methods. We illustrate the broad applicability of the approach in a model of the global oil market identified using a rich set of sign, elasticity and narrative restrictions.