Greece has the largest underground economy in the eurozone and one of the largest in Europe and the OECD countries. On the other hand, Greece is notoriously known for its sizable and widespread tax evasion primarily because of the large number of self employed and its wide geographical distribution. As documented by many studies, the two depend on a corrupted, inefficient and ineffective public administration. The emphasis is here on the restructuring of the Greek tax system taking into consideration these three structural characteristics of the Greek economy: a large informal sector, a pervasive tax evasion and a corrupt public sector (including the tax authorities). Many attempts to change these structural characteristics have failed primarily because they underestimate the costs and overestimate the benefits of any reform. And this because they assume that people’s attitudes (tax morale) and the role institutions can change by a government decree. This paper takes these as givenand proposes a tax system that is based exclusively on wealth (property, bank deposits, shares etc) and the abolishment of VAT and all kinds of income taxes. It is argued that this system is more efficient, more effective, more democratic and promotes competitiveness and economic growth.