Anonymous hiring restricts the information available to hiring managers, potentially creating a trade-off between equity and hiring efficiency. We leverage a pilot program by the City of Helsinki in which hiring for some, but not all, job titles was subject to anonymization. We find that applicants with immigrant background were more likely to be hired without detrimental effects on job turnover or wages. Announcing anonymization increased job applications, but not by groups that ex-post had the most to gain. Our results suggest anonymization can be an effective anti-discrimination policy at least when it's mandated and not voluntary for hiring managers.