The peer review process is central to the scientific method, the advancement and spread of research, as well as crucial for individual careers. However, the single-blind review mode currently used in most Software Engineering (SE) venues is susceptible to apparent and hidden biases, since reviewers know the identity of authors. We perform a study on the benefits and costs that are associated with introducing double- blind review in SE venues. We surveyed the SE community’s opinion and interviewed experts on double-blind reviewing. Our results indicate that the costs, mostly logistic challenges and side effects, outnumber its benefits and mostly regard difficulty for authors in blinding papers, for reviewers in understanding the increment with respect to previous work from the same authors, and for organizers to manage a complex transition. While the surveyed community largely consents on the costs of DBR, only less than one-third disagree with a switch to DBR for SE journals, all SE conferences, and, in particular, ICSE; the analysis of a survey with authors of submitted papers at ICSE 2016 run by the program chairs of that edition corroborates our result.