In spite of enthusiastic encouragements, theories of entrepreneurship still poorly explain the influence of physiological resources and dynamics on entrepreneurs' abilities to perform cognitive tasks known to enable entrepreneurial action. To advance research in this area, we develop and test new theoretical notions about sleep's effects on entrepreneurs' abilities to imagine promising new venture ideas, and to form initial beliefs about the attractiveness of such ideas. Results from three studies, including a self-comparison study over time and a randomized sleep deprivation experiment, show that a good night of sleep positively influences entrepreneurs' abilities to perform cognitive tasks at the very basis of entrepreneurial pursuits, whereas shortchanging sleep can yield suboptimal performance.