Size-discovery mechanisms allow large quantities of an asset to be exchanged at a price that does not respond to price pressure. Primary examples include "workup" in Treasury markets, "matching sessions" in corporate bond and CDS markets, and block-trading "dark pools" in equity markets. By freezing the execution price and giving up on market-clearing, size-discovery mechanisms overcome concerns by large investors over their price impacts. Price-discovery mechanisms clear the market, but cause investors to internalize their price impacts, inducing costly delays in the reduction of position imbalances. We show how augmenting a price-discovery mechanism with a size-discovery mechanism improves allocative efficiency.