We compute optimal mechanism designs for each of a sequence of size-discovery sessions, at which traders submit reports of their excess inventories of an asset to a session operator, which allocates transfers of cash and the asset. The mechanism design induces truthful reports of desired trades and perfectly reallocates the asset across traders. Between sessions, in a dynamic auction market, traders strategically lower their price impacts by shading their bids, causing socially costly delays in rebalancing the asset across traders. As the expected frequency of size-discovery sessions is increased, market depth is further lowered, offsetting the efficiency gains of the size-discovery sessions. Adding size-discovery sessions to a double-auction market has no social value, beyond that of an initializing session. If the mechanism design relies on the double-auction market for information from prices, bidding incentives are further weakened, strictly reducing overall market efficiency.