Curiosity plays a key role in directing learning throughout the lifespan. Prior work finds that violations of expectations can be powerful triggers of curiosity in both children and adults, but it is unclear which expectation-violating events induce the greatest curiosity and how this might vary over development. Some theories have suggested a U-shaped function such that stimuli of moderate extremity pique the greatest curiosity. However, expectation-violations vary not only in degree, but in kind: for example, some things violate an intuitive theory (e.g., an alligator that can talk) and others are merely unlikely (e.g., an alligator hiding under your bed). Combining research on curiosity with distinctions posited in the cognitive science of religion, we test whether minimally counterintuitive (MCI) stimuli, which involve one violation of an intuitive theory, are especially effective at triggering curiosity. We presented adults (N = 77) and 4- and 5-year-olds (N = 36) in the United States with stimuli that were ordinary, unlikely, MCI, and very counterintuitive (VCI) and asked which one they would like to learn more about. Adults and 5-year-olds chose Unlikely over Ordinary and MCI over Unlikely, but not VCI over MCI, more often than chance. Our results suggest that (i) minimally counterintuitive stimuli trigger greater curiosity than merely unlikely stimuli, (ii) surprisingness has diminishing returns, and (iii) sensitivity to surprisingness increases with age, appearing in our task by age 5.