Human judgment often violates normative standards, and virtually no judgment error has received as much attention as the conjunction fallacy. Judgment errors have historically served as evidence for dual-process theories of reasoning, insofar as these errors are assumed to arise from reliance on a fast and intuitive mental process, and are corrected via effortful deliberative reasoning. In the present research, three experiments tested the notion that conjunction errors are reduced by effortful thought. Predictions based on three different dual-process theory perspectives were tested: lax monitoring, override failure, and the Tripartite Model. Results indicated that participants higher in numeracy were less likely to make conjunction errors, but this association only emerged when participants engaged in two-sided reasoning, as opposed to one-sided or no reasoning. Confidence was higher for incorrect as opposed to correct judgments, suggesting that participants were unaware of their errors.