Most document-extraction systems use a single model for all documents. This is simple but can be costly for easy cases and less effective for difficult ones. We examine whether we can predict a document's difficulty before extraction using inexpensive, document-based signals, and use this to choose between a cheaper and a stronger extractor. We find that routing only helps if two conditions hold: the cheaper model fails often enough to make routing worthwhile, and those failures can be predicted from visible features such as image quality and layout. We turn these into a practical test and apply it to five genres. When both conditions are met, the calibrated router reduces cost by 31-33% on receipts and 77% on degraded ad-buy forms while keeping quality within 0.02 F1 of always choosing the large model. Routing does not help if either condition is missing, as with clean digital invoices or nutrition labels that are already easy to read. A small labeled pilot can predict whether routing will work, and in the two cases where we ran it first, the prediction was correct. A simple bag-of-words router works about as well as engineered features, showing that the main limit is the genre, not the router design; we use interpretable features to help explain which genres can be routed. The router must be retrained for each dataset and does not transfer across datasets, even within the same genre. These results hold for two model pairs with cost differences of 5x and 3x.

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