Over-the-counter markets are at the center of the global reform of the financial system. We show how the size and structure of these markets can undergo rapid and extensive changes when participants engage in portfolio compression, which is an optimization technology that exploits multilateral netting opportunities. We find that tightly knit and concentrated trading structures, as featured by many large over-the-counter markets, are especially susceptible to reductions of notional amounts and network reconfigurations resulting from compression activities. Using a unique transaction-level data set on credit-default-swaps markets, we estimate reduction levels, suggesting that the adoption of this technology can account for a large share of the historical development observed in these markets since the global financial crisis. Finally, we test the effect of a mandate to centrally clear over the counter markets in terms of size and structure. When participants engage in both central clearing and portfolio compression with the clearinghouse, we find large netting failures if clearinghouses proliferate. Allowing for compression across clearinghouses by and large offsets this adverse effect.