Random Field Theory (RFT) is a computationally efficient means of analysing neuroimaging data that has been widely applied to control false positives via cluster, peak and voxel level inference. However it has historically relied on a number of key assumptions including smoothness and stationarity which are unlikely to hold in practice. We propose improved RFT methods which drop both of these key assumptions and provide exact (instead of conservative) false positive rate control for voxelwise inference.