The purpose of this paper is to present an exercise where we identify optimal income tax rules according to various social welfare criteria, keeping fixed the total net tax revenue. Empirical applications of optimal taxation theory have typically adopted analytical expressions for the optimal taxes and then imputed numerical values to their parameters by using “calibration” procedures or previous econometric estimates. Besides the restrictiveness of the assumptions needed to obtain analytical solutions to the optimal taxation problem, a shortcoming of that procedure is the possible inconsistency between the theoretical assumptions and the assumptions implicit in the empirical evidence. In this paper we follow a different procedure, based on a computational approach to the optimal taxation problem. To this end, we estimate a microeconomic model with 78 parameters that capture heterogeneity in consumption-leisure preferences for singles and couples as well as in job opportunities across individuals based on detailed Norwegian household data for 1994. For any given tax rule, the estimated model can be used to simulate the labour supply choices made by single individuals and couples. Those choices are therefore generated by preferences and opportunities that vary across the decision units. We then identify optimal tax rules – within a class of 9-parameter piece-wise linear rules - by iteratively running the model until a given social welfare function attains its maximum under the constraint of keeping constant the total net tax revenue. The parameters to be determined are an exemption level, four marginal tax rates, three “kink points” and a lump sum transfer that can be positive (benefit) or negative (tax). We explore a variety of social welfare functions with differing degree of inequality aversion. All the social welfare functions imply monotonically increasing marginal tax rates. When compared with the current (1994) tax systems, the optimal rules imply a lower average tax rate. Moreover, all the optimal rules imply – with respect to the current rule – lower marginal rates on low and/or average income levels and higher marginal rates on relatively high income levels. These results are partially at odds with the tax reforms that took place in many countries during the last decades. While those reforms embodied the idea of lowering average tax rates, the way to implement it has typically consisted in reducing the top marginal rates. Our results instead suggest to lower average tax rates by reducing marginal rates on low and average income levels and increasing marginal rates on very high income levels.