This note questions two emerging views on ways to tackle systemic risk. As evidenced by the explosive growth of investment banks, which were regulated more lightly because they were assumed to be systemically less important, regulatory unevenness can trigger acutely destabilizing regulatory arbitrage. Hence, unless systemic footprints can be accurately measured and updated, something we think is unlikely, regulating differentially those institutions that are deemed to be the most systemically relevant looks like a perilous return to the past. Similarly, internalizing systemic liquidity risk by taxing maturity mismatches looks like a remnant of idiosyncratic thinking. Matching short liabilities with short assets can protect an individual intermediary's liquidity but at the expense of exacerbating systemic vulnerability.