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Contracting between private health plans and hospitals has been described as "chaos behind a veil of secrecy." We develop a novel algorithm that classifies inpatient claims as one of three contract types-discounted charges, fixed rates, or per diems-and apply it to the 2009-2014 Colorado All Payer Claims Database. Of $1.1 billion in classifiable private health plan payments for inpatient care in Colorado, we find that 42.1% were fixed rates, 41.1% were discounted charges, and 16.0% were per diems. We find wide variation in contract types among private health plans and hospital types, and a pronounced shift over the study period in private plans' contract types, away from discounted charges, and toward fixed rates. To test our algorithm's validity, we apply it to Colorado Medicare and Medicaid claims-both of which are known primarily to pay using fixed rates-and find, reassuringly, that 86.3% of Medicare payments (98.6% when we exclude Medicare claims with special payment rules) and 79.7% of Medicaid payments are classified as fixed rates.