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Money can be tainted when it is associated with direct or indirect harm to others. Deciding whether to accept "dirty money" poses a dilemma because money can be used to help others, but accepting dirty money has moral costs. How people resolve the dilemma of dirty money remains unknown. One theory casts the dilemma as a valuation conflict that can be resolved by integrating the costs and benefits of accepting dirty money. Here, we use behavioral experiments and computational modeling to test the valuation conflict account and unveil the cognitive computations employed when deciding whether to accept or reject morally tainted cash. In Study 1, British participants decided whether to accept "dirty" money obtained by inflicting electric shocks on another person (versus "clean" money obtained by shocking oneself). Computational models showed that the source of the money (dirty versus clean) impacted decisions by shifting the relative valuation of the money's positive and negative attributes, rather than imposing a uniform bias on decision-making. Studies 2 and 3 replicate this finding and show that participants were more willing to accept dirty money when the money was directed towards a good cause, and observers judged such decisions to be more praiseworthy than accepting dirty money for one's own profit. Our findings suggest that dirty money can be psychologically "laundered" through charitable activities and have implications for understanding and preventing the social norms that can justify corrupt behavior.