Because of the high dimensionality of neuroimaging data, identifying a statistical test that is both valid and maximally sensitive is an important challenge. Here, we present a combination of two approaches for functional magnetic resonance imaging (fMRI) data analysis that together result in substantial improvements of the sensitivity of cluster‐based statistics. The first approach is to create novel cluster definitions that optimize sensitivity to plausible effect patterns. The second is to adopt a new approach to combine test statistics with different sensitivity profiles, which we call the min(p) method. These innovations are made possible by using the randomization inference framework. In this article, we report on a set of simulations and analyses of real task fMRI data that demonstrate (a) that the proposed methods control the false‐alarm rate, (b) that the sensitivity profiles of cluster‐based test statistics vary depending on the cluster defining thresholds and cluster definitions, and (c) that the min(p) method for combining these test statistics results in a drastic increase of sensitivity (up to fivefold), compared to existing fMRI analysis methods. This increase in sensitivity is not at the expense of the spatial specificity of the inference.