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Vesting of equity payments to an entrepreneur, which is a form of time-contingent compensation, is very common in venture capital contracts. Empirical research suggests that vesting is used to help overcome asymmetric information and agency problems. We show in a theoretical model that vesting equity to an entrepreneur over a long period of time acts as a screening device against a bad entrepreneur type. But incomplete contracts due to hold-up by the venture capitalist imply that equity compensation, in the form of either short-term or long-term vesting, cannot provide standard contractible equity incentives for the entrepreneur to take an unobservable action involving effort. We introduce a new model of effort based on a verifiable choice of an effort-intensive project, for which the short-term vesting of equity can provide incentives, but which results in a trade-off between incentives and screening. Contingent control rights are a substitute for short-term vesting and provide the largest incentives for effort by fully protecting the entrepreneur from hold-up. We also show that a new link between equity cash flow claims and control rights is that residual equity control rights over the firm are necessary to protect residual equity claims from hold-up.