We study the effects of a phase-in of the liquidity coverage ratios (LCR). We find surprisingly that LCR, while reducing systemic risk in the initial phase, might produce an increase of it in the final phase. First, high LCR reduce the insurance function of interbank markets. Second, when applied equally to all banks LCR impose unnecessary liquidity shortages on banks which are mildly leveraged and which would otherwise act as interbank liquidity providers. Motivated by this result we investigate if imposing LCR differentially across banks and conditional on an index of systemic importance might deliver a better result. Our results show that this simple skewing of requirements toward more systemic banks is highly effective in delivering a more stable system.