Those who are less skilled tend to overestimate their abilities more than do those who are more skilled-the so-called Dunning-Kruger effect. Less-skilled performers presumably have less of the knowledge needed to make informed guesses about their relative performance. If so, the Dunning-Kruger effect should vanish when participants do have access to information about their relative ability and performance. Competitive bridge players predicted their results for bridge sessions before playing and received feedback about their actual performance following each session. Despite knowing their own relative skill and showing unbiased memory for their performance, they made overconfident predictions consistent with a Dunning-Kruger effect. This bias persisted even though players received accurate feedback about their predictions after each session. The finding of a Dunning-Kruger effect despite knowledge of relative ability suggests that differential self-knowledge is not a necessary precondition for the Dunning-Kruger effect. At least in some cases, the effect might reflect a different form of irrational optimism.