In the wake of the replication crisis, there have been calls to increase the clarity and precision of theory in the social sciences. Here, we argue that the effects of these calls may be limited due to incentives favoring ambiguous theory. Intentionally or not, scientists can exploit theoretical ambiguities to make support for a claim appear stronger than it is. Practices include theory stretching, interpreting an ambiguous claim more expansively to absorb data outside of the scope of the original claim, and post-hoc precision, interpreting an ambiguous claim more narrowly so it appears more precisely aligned with the data. These practices lead to the overestimation of evidence for the original claim and create the appearance of consistent support and progressive research programs, which may in turn be rewarded by journals, funding agencies, and hiring committees. Selection for ambiguous research can occur even when scientists act in good faith. Although ambiguity might be inevitable or even useful in the early stages of theory construction, scientists should aim for increased clarity as knowledge advances. Science benefits from transparently communicating about known ambiguities. To attain transparency about ambiguity, we provide a set of recommendations for authors, reviewers, and journals. We conclude with suggestions for research on how scientists use strategic ambiguity to advance their careers and the ways in which norms, incentives, and practices favor strategic ambiguity. Our paper ends with a simple mathematical model exploring the conditions in which high-ambiguity theories are favored over low-ambiguity theories, providing a basis for future analyses.