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This paper finds that firms that have substantially increased leverage are more likely to issue convertible debt than firms that have increased leverage only slightly. Also, firms that have substantially decreased leverage are more likely to issue convertible debt than firms that have decreased leverage only slightly. Since only firms that had been highly leveraged in the past can substantially decrease leverage, this second result suggests that bondholders also demand greater protection from firms that either increased leverage in the past or began highly leveraged. Together, these results suggest that a firm's past behavior is important to bondholders.