We investigate how liquidity providers (LPs) choose between trading venues with high and low fees, in the face of a fixed common gas cost. Analyzing Uniswap data, we find that  high-fee pools attract 58% of liquidity supply but execute only 21% of trading volume. Large LPs dominate low-fee pools, frequently adjusting positions in response to substantial trading volume. In contrast, small LPs converge to high-fee pools, accepting lower execution probabilities to mitigate smaller liquidity management costs. Fragmented liquidity dominates a single-fee market, as it encourages more liquidity providers to enter the market, while enhancing LP competition on the low-fee pool.