While hiring discrimination against disabled candidates is widely documented, the reasons for such discrimination and the mechanisms designed to reduce it are not well understood. This study aims to tackle these questions through a large-scale correspondence study. Fictitious job applications were sent to about 4,000 job vacancies for accountants and financial accounts assistants in the UK. Consistent with discrimination, we find a 5.6 percentage point (15%) gap in the employer callback rate associated with mobility impairment indicated by the use of a wheelchair, but substantial occupational heterogeneity. Productivity signals designed to reduce statistical discrimination, including the offer of a positive reference from a previous employer and, enhanced education and technical skills, do not reduce, and actually widen, the disability gap in callbacks. Our findings are suggestive of taste-based discrimination being a significant barrier to employment for disabled people that requires policy attention.