Non-uniform indirect taxes treat equals and those unequal differently (horizontal inequity and vertical redistribution). Horizontal inequity is caused by taste differences among similar households, but some excises are designed to reflect social, not revealed, preferences. We apply two methodologies for decomposing the overall redistributive effect of the present and three alternative indirect tax structures into vertical and horizontal effects for Greece, using the 1998-99 Household Expenditure Survey micro-database. In all cases, the taste component is considerable, even when we allow for social preferences, while improvements in vertical redistribution can be achieved, albeit at the cost of increased horizontal inequity. Copyright (c) 2008 The Authors Journal compilation (c) Institute for Fiscal Studies, 2008.