This paper compares the performance of Bayesian variable selection approaches for spatial autoregressive models. It presents two alternative approaches that can be implemented using Gibbs sampling methods in a straightforward way and which allow one to deal with the problem of model uncertainty in spatial autoregressive models in a flexible and computationally efficient way. A simulation study shows that the variable selection approaches tend to outperform existing Bayesian model averaging techniques in terms of both in-sample predictive performance and computational efficiency. The alternative approaches are compared in an empirical application using data on economic growth for European NUTS-2 regions.