Organizations increasingly deploy autonomous artificial intelligence (AI) systems for operational decisions, such as inventory replenishment. Yet granting full override discretion can degrade performance because of human bias and judgment errors, while prohibiting overrides may overlook valuable private information. This raises a key question: How should override discretion be structured to improve human supervision of autonomous AI? We propose a constrained override policy that limits the number of overrides within each decision episode. When the constraint binds, humans prioritize overrides they consider most valuable, a process we call selective filtering. We evaluate the policy in a smart-vending field experiment, randomly assigning 553 workers to no, free, or constrained downward override, with the constrained policy capped at two stock-keeping units (SKUs) per machine replenishment. Relative to the no-override policy, free override reduces inventory by 1.95 log points but also lowers sales by 1.19 log points, whereas constrained override reduces inventory by 1.28 log points without a statistically significant sales decline. Local average treatment effect estimates support this contrast. Constrained override also reduces inventory without statistically significant sales losses among experienced workers, for top-sales and growth-stage SKUs, and with greater machine--SKU familiarity. Simulations suggest calibrating the cap to the firm's relative margin, worker experience, and machine--SKU familiarity. Constrained override offers a simple and scalable way to use workers' private information in inventory replenishment. Firms can limit override discretion through the replenishment interface without redesigning the algorithm, identifying useful overrides in advance, providing individualized feedback, or retraining workers.

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