Performance thresholds are commonly used in executive compensation contracts. We examine the contractual nonlinearity associated with performance thresholds and its incentive implications. Incorporating a performance threshold into a standard principal‐agent model of a linear contract, we show that pay schemes using a performance threshold are optimal. By truncating a linear scheme at poor performance, the threshold mitigates agency costs associated with the downside risk of production. Examining CEO compensation data, we find evidence of the role of performance thresholds. As a consequence of under‐threshold performance, the tobit estimator is shown to increase pay‐performance sensitivity, notably improving upon the standard OLS estimator.