This study uses laboratory markets to determine how different types of information or different market structures influence a markets informational efficiency. Unlike secondary data studies of market efficiency, in a laboratory the efficiency of a market can be measured without reference to an asset pricing model. Specifically, in an efficient market the price is identical to the price that would arise in an otherwise identical economy in which all information is fully disseminated. While secondary data studies must model the efficient price (or return), the efficient price can be observed directly in a laboratory by creating the “otherwise identical” economy. I compare the efficiency of two information structures and two market structures. The two information structures differ by whether or not there is aggregate certainty in the market; that is, whether or not the union of all traders’ information sets perfectly identifies the value of the risky asset. All previous experimental research into market efficiency has used markets with aggregate certainty. However, many of the difficulties of decision making under uncertainty disappear when the information in the market collectively reveals the asset’s payoff. I find that prices in markets with aggregate uncertainty are very inefficient throughout the market. If traders could take the appropriate position in the market and trade later at the efficient market price the average abnormal return would be 27% in the final years of the market. In contrast, prices in the markets with aggregate certainty are very efficient during the final years, with an average abnormal return of only 3%. 1 also manipulate the number of traders in the market. It is sometimes argued that markets are efficient because there are a “large number” of traders and their individual errors average out. I find that the number of traders has no significant impact on the efficiency of final prices in the market, but markets with only a few traders converge to the efficient price much more quickly within a trading period than markets with many traders. This appears to occur because there is a greater dispersion of risk preferences in markets with many traders, and traders with extreme preferences engage in transactions that are primarily a function of their preferences rather than their information. Consequently, the markets with many traders have more “noisy” transactions, making it more difficult to infer information from the market data.