We use a behavioural microsimulation model embedded in a numerical optimization procedure in order to identify optimal (social welfare maximizing) tax-transfer rules. We consider the class of tax-transfer rules consisting of a universal basic income and a tax defined by a 4th degree polynomial. The rule is applied to total taxable household income. A microeconometric model of household, which simulates household labour supply decisions, is embedded into a numerical routine in order to identify – within the class defined above – the tax-transfer rule that maximizes a social welfare function. We present the results for five European countries: France, Italy, Luxembourg, Spain and United Kingdom. For most values of the inequality aversion parameter, the optimized rules provide a higher social welfare than the current rule, with the exception of Luxembourg. In France, Italy and Luxembourg the optimized rules are significantly different from the current ones and are close to a Negative Income Tax or a Universal basic income with a flat tax rate. In Spain and the UK, the optimized rules are instead close to the current rule. With the exception of Spain, the optimal rules are slightly disequalizing and the social welfare gains are due to efficiency gains. Nonetheless, the poverty gap index tends to be lower under the optimized regime.