In this paper, we show both theoretically and empirically that the size of over-the-counter (OTC) markets can be reduced without affecting individual net positions. First, we find that the networked nature of these markets generates an excess of notional obligations between the aggregate gross amount and the minimum amount required to satisfy each individual net position. Second, we show conditions under which such excess can be removed. We refer to this netting operation as compression and identify feasibility and effciency criteria, highlighting intermediation as the key element for excess levels. We show that a trade-off exists between the amount of notional that can be eliminated from the system and the conservation of original trading relationships. Third, we apply our framework to a unique and comprehensive transaction-level dataset on OTC derivatives including all firms based in the European Union. On average, we find that around 75% of market gross notional relates to excess. While around 50% can in general be removed via bilateral compression, more sophisticated multilateral compression approaches are substantially more effcient. In particular, we find that even the most conservative multilateral approach which satisfies relationship constraints can eliminate up to 98% of excess in the markets.