Influence practitioners often highlight a target's achievements (e.g., "she is the city's top-rated chef"), but recent research reveals that highlighting a target's potential (e.g., "she could become the city's top-rated chef") can be more effective. We examine whether the uncertainty inherent in potential is crucial to its appeal by exploring whether the preference for potential depends on individual and situational differences in tolerance for uncertainty. In two studies in two different categories (comedians and restaurants), we measure and manipulate tolerance for uncertainty to show that the preference for potential emerges when tolerance for uncertainty is high, but not low. We further show that the uncertainty surrounding potential fosters greater interest and deeper processing when tolerance for uncertainty is high, which in turn promotes more favorable reactions. Thus, the current research reveals when and why emphasizing potential is more effective than emphasizing achievement, illuminating the key role of uncertainty in driving this effect.