Tax non-filing is legal in more than thirty countries worldwide. Using German administrative tax data, we examine the effect of such optional (non-)filing systems: Low-income taxpayers are both more likely not to file and to over-remit taxes, aggregating to total over-remittances of 950 millione in 2014. Because low-income non-filers face higher effective average tax rates, this reduces the effective tax progressivity. Non-filing also increases effective marginal tax rates which imposes distortionary effects for non-filers with no mechanical tax revenue gain from other taxpayers, leading to unexploited tax revenue potential. We suggest two reform proposals to quantify this potential.