The historical turn in social science has prompted scholars to engage with the work of historians on a large scale. Here, social scientists face two standard problems of selection bias: confirmation bias and convenience sampling. So far, the record of dealing with these problems has been poor, and little has been done to specify how social scientists can sift a broader body of historiography. We present a criterial framework that describes how social scientists can mitigate bias when using historical studies. We term the idea behind this framework the Ulysses Principle because it can be understood as a way of avoiding the siren call of confirmation bias when using historical sources as the primary evidentiary base. The framework includes considerations about conceptual consistency, the theoretical vantage points of historical sources, and updated evidence. The three criteria and the trade-offs between them are illustrated using two recent examples from comparative historical analyses.