This paper introduces a method which permits valid inference given a finite number of heterogeneous and highly-correlated clusters. Permitting strong correlations across clusters may be crucial for proper inference and panel data estimation methods can potentially induce such correlations. While many inference methods assume clusters are asymptotically independent or model dependence across clusters as a function of a distance metric, such restrictions are unnecessary given panel data. This paper proposes estimating cross-cluster dependence by studying co-movements between clusters and then isolating the independent component of each cluster. The method is computationally inexpensive, can be employed for linear and nonlinear estimators, and does not require prior knowledge of which clusters are correlated or even the existence of independent clusters. The approach is valid for large T or large N. In simulations, the procedure rejects at appropriate rates even in the presence of highly-correlated clusters.