We study whether a redesign of the social security and income tax-and-transfer systems can deliver significant welfare gains. Our rich quantitative model features both realistic inequality over the life-cycle and the key main channels through which redistributive policies can distort aggregate allocations. We find that there are two distinct ways to achieve significant welfare gains with joint policy reforms. The first prioritizes reducing distortions through a regressive pension system, resulting in higher inequality. The second reduces inequality through progressive pensions, complemented with a less progressive tax system to mitigate the rise in distortions. In both reform types, pension progressivity emerges as the most powerful instrument, either to manage distortions or to redistribute income within generations. Since redistributive instruments turn out to be highly distortionary in our benchmark economy, utilitarian social welfare is maximized through a reduction in distortions.