Acquiring abilities in the absence of a task-oriented reward function is at the frontier of reinforcement learning research. This problem has been studied through the lens of empowerment, which draws a connection between option discovery and information theory. Information-theoretic skill discovery methods have garnered much interest from the community, but little research has been conducted in understanding their limitations. Through theoretical analysis and empirical evidence, we show that existing algorithms suffer from a common limitation -- they discover options that provide a poor coverage of the state space. In light of this, we propose Explore, Discover and Learn (EDL), an alternative approach to information-theoretic skill discovery. Crucially, EDL optimizes the same information-theoretic objective derived from the empowerment literature, but addresses the optimization problem using different machinery. We perform an extensive evaluation of skill discovery methods on controlled environments and show that EDL offers significant advantages, such as overcoming the coverage problem, reducing the dependence of learned skills on the initial state, and allowing the user to define a prior over which behaviors should be learned.