The advantage of multiple sourcing to protect against supplier failures arising from undependable products due to latent defects is examined using a model with non-linear external failure costs. Prior research has focused only on supplier failures arising from unreliable supply, such as late/insufficient/no delivery. I derive a closed-form characterization of the optimal production quota allocation for the LUX (Latent defect-Undependable product-eXternal failure) setting. The allocation determines the optimal supply base, with intuitive properties that hold under a mild condition. The condition includes the special case of equal procurement costs charged by suppliers but also allows unequal costs without any particular order. Necessary and sufficient conditions are also derived to determine (i) the exact size of the optimal supply base, provided the mild condition holds, and (ii) whether single or multiple sourcing is optimal, without requiring any precondition. With minor modifications, the results also hold when a buyer-initiated procurement contract can be used to elicit the private information on the suppliers’ unit variable production costs.