People’s perceptions of their intelligence correlate only moderately with objective intelligence measures. On average, people overestimate themselves. According to the popular Dunning-Kruger effect, this is particularly true for low performers: Across many domains, those in the lowest quantile overestimate their abilities the most. However, recent work using improved statistical approaches found little support for a Dunning-Kruger effect in general intelligence. We investigated the accuracy of and Dunning-Kruger effects in self-estimates of general, verbal, numerical, and spatial intelligence—domains that differed in how well they can be judged in the past. 281 participants completed self-estimates and intelligence measures online. Self-estimates showed mostly moderate correlational accuracy that was slightly higher for numerical intelligence and lower for verbal intelligence. Across domains, participants rated their intelligence as above-average. However, as their intelligence was indeed high, this was not an overestimation. While standard analyses indicated Dunning-Kruger effects in three out of four measures, improved statistical methods only yielded some support for one in verbal intelligence: People with lower verbal intelligence tended to have less self-knowledge about it. The generalizability of these findings is limited to young, highly educated populations. Nevertheless, our results contribute to a growing literature questioning the generality of the Dunning-Kruger effect.