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Abstract Neural networks were previously applied to reconstruct climate indices from tree rings but showed mixed results in skill relative to more standard linear methods. A two‐layer neural network is explored for purposes of reconstructing summertime self‐calibrated Palmer Drought Severity Index (scPDSI) across the contiguous United States. Reconstructions using neural networks are more skillful than a linear approach at 75% of the gridboxes if evaluated by the coefficient of efficiency and at 54% when using the Pearson correlation coefficient. The increased reconstruction skill is related to the network capturing nonlinear growth‐climate relationships. In the Southwest, in particular, a nonlinear response function captures a diminishing sensitivity of growth to moisture under wetter conditions, consistent with alleviation of moisture stress. These results indicate somewhat less‐severe and more‐stable incidences of drought over the past two centuries in the U.S. Southwest.