We study optimal trading across a limit-order book and an automated market maker. We determine the “effective liquidity” available to a large trader on both venues, when arbitrageurs immediately exploit intra-exchange price differences but only gradually offset the price impact of aggregate trade imbalances. The resulting price impact dynamics are nonlinear, but risk-neutral optimization problems can still be reduced to simple pointwise maximizations by “passing to impact space”. These results are illustrated with an empirical case study for ETH/USDC price and trade data from Binance and Uniswap.