Conventional methods for cluster-robust inference are inconsistent when clusters of unignorably large size are present. We formalize this issue by deriving a necessary and sufficient condition for consistency, a condition frequently violated in empirical studies. Specifically, 77% of empirical research articles published in American Economic Review and Econometrica during 2020–2021 do not satisfy this condition. To address this limitation, we propose two alternative approaches: (i) score subsampling and (ii) sizeadjusted reweighting. Both methods ensure uniform size control across broad classes of data-generating processes where conventional methods fail. The first approach (i) has the advantage of ensuring robustness while retaining the original estimator. The second approach (ii) modifies the estimator but is readily implementable by practitioners using statistical software such as Stata and remains uniformly valid even when the cluster size distribution follows Zipf’s law. Extensive simulation studies support our findings, demonstrating the reliability and effectiveness of the proposed approaches.