Most assets clear independently rather than jointly. This paper presents a model based on the uniform‐price double auction which accommodates arbitrary restrictions on market clearing, including independent clearing across assets (allowed when demand for each asset is contingent only on the price of that asset) and joint market clearing for all assets (required when demand for each asset is contingent on the prices of all assets). Additional trading protocols for traded assets—neutral when the market clears jointly—are generally not redundant innovations, even if all traders participate in all protocols. Multiple trading protocols that clear independently can be designed to be at least as efficient as joint market clearing for all assets. The change in price impact brought by independence in market clearing can overcome the loss of information, and enhance diversification and risk sharing. Except when the market is competitive, market characteristics should guide innovation in trading technology.