Do people anticipate the conditions that enable them to manipulate their beliefs when confronted with unpleasant information? We investigate whether individuals seek out the "cognitive flexibility" needed to distort beliefs in self-serving ways, or instead attempt to constrain it, committing to unbiased judgment. Experiments with 6500 participants, including financial and legal professionals, show that preferences are heterogeneous: over 40% of advisors prefer flexibility, even if costly. Actively seeking flexibility does not preclude belief distortion. Individuals anticipate the effects of cognitive flexibility and their choice to pursue it responds to incentives, suggesting some sophistication about the cognitive constraints to belief distortion.