I analyze a multi-asset market under two trading mechanisms. In the first (the unrestricted system), traders' demand for each asset depends on all equilibrium prices and prices reflect the information contained in all order flows; in the second (the restricted system), traders' demand depends on the traded asset price and prices reflect single order flow information. I show that informed traders' use of multi-dimensional private information depends on the number of prices they observe, and on the price formation process. I then give conditions rendering the restricted system more efficient than the unrestricted system.