Payer (insurer) sharing of savings is a way of motivating providers of medical services to reduce cost growth. A Medicare shared savings program is established for accountable care organizations in the 2010 Patient Protection and Affordable Care Act. However, savings created by providers cannot be distinguished from the normal (random) variation in medical claims costs, setting up a classic principal–agent problem. To lessen the likelihood of paying undeserved bonuses, payers may pay bonuses only if observed savings exceed minimum levels. We study the trade-off between two types of errors in setting minimum savings requirements: paying bonuses when providers do not create savings and not paying bonuses when providers create savings. Copyright © 2011 John Wiley & Sons, Ltd.