Discrimination in hiring is a persistent issue leading to inefficient labour markets. Several policies have been suggested to tackle these issues with varying degrees of effectiveness. In this paper we induce statistical discrimination in hiring decisions in the lab and test whether "blind hirings" (i.e. removing all identifying characteristics in the initial stages of the hiring process) can address these inefficiencies. The results from a lab experiment conducted at the University of Cyprus with 144 students suggest that this type of policy can only be effective if the formerly discriminated group is sufficiently small. If on the other hand the group is large, it may lead to less overall hiring and further losses in welfare. Equality in hiring may be achieved, but the economy experiences an overall loss in welfare, mostly incurred by the previously advantaged group. Blind hirings can therefore be beneficial (both in Utilitarian and Rawlsian terms) if the disadvantaged group is a minority. The mechanism behind this may be related to "adaptive beliefs", i.e. that agents act based on beliefs that have been formed through past experience, even if that action may be considered economically irrational in the absence of belief formation.