We develop an extended version of Roemer's Equality of Opportunity (EOp) criterion that accounts for income differentials between as well as within types, where types are defined by circumstances that are beyond people's control (parental education, in this study). A microeconometric model of labour supply in Italy is employed to identify income tax-transfer rules that are optimal according to the extended EOp criterion. Overall, the results do not conform to the perhaps common expectation that the more conventional Equality of Outcome criterion is more supportive of 'interventionist' (redistributive) policies than the EOp approach. [ABSTRACT FROM AUTHOR]