VAT is normally considered to have regressive distributional effects on income distribution. Many countries try to address distributional concerns with rate differentiation. Based on Swiss data we find that both the existing VAT as well as a revenue-neutral flat rate have no significant redistributive effects on the Gini coefficient. Further, we show that differentiated VAT rates only have weak intended distributional effects and that a different VAT structure can also not make VAT progressive regarding income. Based on our results, we conclude that introducing a flat rate should be considered.