In neuroimaging cluster-based inference has generally been found to be more powerful than voxel-wise inference. However standard cluster-based methods assume stationarity (constant smoothness), while under nonstationarity clusters are larger in smooth regions just by chance, making false positive risk spatially variant. Hayasaka et al. proposed a Random Field Theory (RFT) based nonstationarity adjustment for cluster inference and validated the method in terms of controlling the overall family-wise false positive rate. The RFT-based methods, however, have never been directly assessed in terms of homogeneity of local false positive risk. In this work we propose a new cluster size adjustment that accounts for local smoothness, based on local empirical cluster size distributions and a two-pass permutation method. We also propose a new approach to measure homogeneity of local false positive risk, and use this method to compare the RFT-based and our new empirical adjustment methods. We apply these techniques to both cluster-based and a related inference, threshold-free cluster enhancement (TFCE). Using simulated and real data we confirm the expected heterogeneity in false positive risk with unadjusted cluster inference but find that RFT-based adjustment does not fully eliminate heterogeneity; we also observe that our proposed empirical adjustment dramatically increases the homogeneity and TFCE inference is generally quite robust to nonstationarity.