Although people lie often, and mostly for self-serving reasons, they do not lie as much as they could. The “fudge factor” hypothesis suggests that one reason for people not to lie is that they do not wish to self-identify as liars. Accordingly, self-serving lies should be more likely when they are less obvious to the liars themselves. Here we show that the likelihood of self-serving lies increases with the probability of accidentally telling the truth. Players in our game could transmit sincere or insincere recommendations to their competitors. In line with the fudge factor hypothesis, players lied when their beliefs were based on flimsy evidence and did not lie when their beliefs were based on solid evidence. This is the first demonstration of a new moral hypocrisy paradox: People are more likely to be insincere when they are more likely to accidentally tell the truth.