The numerous studies on preferences for redistribution in recent years offers a wealth of insights into the interactions between institutions and economic outcomes. In this paper I posit that labour market institutions can be and have been used to mitigate the regressive effects of market failures in education and in the provision of employment insurance and offer empirical evidence on OECD countries supporting this view. It is argued that people's perception of the fairness of market and non-market institutions affects both the demand for redistribution and the choice of the instruments to achieve it. The analysis is retrospective but may help to assess the future impact on inequality of labour market reforms in those European countries still sharing solidaristic social preferences. The main policy stance envisaged in the paper is that since social transfers and unemployment protection are substitutes in the generation of social insurance and redistribution, to offset the regressive impact of labour deregulation, appropriate unemployment benefit schemes or universal systems of social protection should be improved or instituted. Finally, any forward-looking reform of the welfare systems aiming to increase labour market flexibility should channel more money to education and training programs.