Permutation tests are increasingly used as a reliable method for inference in neuroimaging. However, they are computationally intensive, and can be prohibitively slow for large, complex models. However, properties of statistics used with the general linear model (GLM) and their distributions can be exploited to obtain accelerations irrespective of generic software or hardware improvements. The following approaches will be discussed: (i) performing a small number of permutations; (ii) estimating the p-value as a parameter of a negative binomial distribution; (iii) fitting a generalised Pareto distribution to the tail of the permutation distribution; (iv) computing p-values based on the expected moments of the permutation distribution, approximated from a gamma distribution; (v) direct fitting of a gamma distribution to the empirical permutation distribution; (vi) permuting a reduced number of voxels, with completion of the remainder using low rank matrix theory. Performance of these methods with both synthetic and real data from an imaging experiment will be presented.