A redistribution of welfare can best be realized by lump sum transfers, but since such transfers require complete information by the government on preferences and resources of all agents, it is not possible in practice. Taxation (and subventions) of commodities and incomes is an alterative way for redistribution, by which however no Pareto efficient allocation is attained. This is all well known. The first question which is attacked in this paper is: do there exist other allocation mechanisms that achieve a better redistribution than taxes? This problem is studied with the help of a simple model: agents have an identical cardinal utility function \(u(x_ i,\theta_ i)\), permitting interpersonal comparison of utility; \(x_ i\) is a consumption vector and \(\theta_ i\) a taste parameter, which cannot be observed by the government. Government intends to maximize \(\int U(x,\theta) f(\theta) d\theta\), where f(\(\theta)\) is the (known) distribution of the taste parameter. It is shown that allocation mechanisms under the three alternative behavioural assumptions of dominant strategies, Bayesian strategies and Nash strategies do not perform better than taxes. Secondly the question is discussed, whether as an alternative to commodity and income taxes, taxation could be based on indices that depend on the current choices of the agents. Clearly under such a tax scheme agents will adjust their behaviour, in order to modify the observed index, that is, they will manipulate the index. The performance of the scheme is shown to depend on the correlation between index and taste parameter and on the cost of manipulation, i.e., the utility loss of agents due to the manipulation of the index. Finally indices are studied that depend on past choices. The observed history of choices might give better information on the tastes. However it is shown in a simple example that taxation of those indices may be highly inefficient, because agents will choose in such a way as to hide their tastes.