The Expert Committee on Pension Reform (2014-2017) did no comprehensive analysis of the Czech pension system and did not discuss any comprehensive pension reform. Just before the last meeting of this Committee the opinions were expressed that no pension reform is necessary – after the cancellation of the fully unsuccessful new retirement savings pillar and after some marginal parametric changes of the public and personal pensions. Although domestic and foreign recommendations are enough in this direction. The paper demonstrates that the 2010 ruling of the Czech Constitutional Court was not implemented duly by the then government: the system of public pensions continues to be unconstitutional and incomprehensible for its addresses. Moreover, the system of private pensions and pension savings is also unconstitutional and insufficiently comprehensible. The paper presents a systemic analysis of the public “pension insurance” and supplementary pension savings products and indicates potential alternatives of both these systems which would not, if possible, change the amounts of assessed pensions and of state support and which would result in their constitutionality and comprehensibility. The expected consequence of such a technical reform is a strongly increase of the rationality of the behaviour of the current and potential participants of these systems. At the same time a technical reform of wage taxation may be implemented.