This study contains data that throw substantial doubt upon the applicability of the random walk model to stock prices. Samples of the books of the specialist indicate that stock market decision makers place their limit and stop orders at numbers with which they are accustomed to deal. Congestion of limit orders, in combination with the specialist's reluctance to trade for his own account, creates a situation where higher priced issues trade mainly at the integers. Six samples of two hundred low priced issues unchanged for the day, and two samples of issues stationary until noon, indicate that these prices settle at the round numbers. Intelligent trading of floor traders and specialists causes the ratio of highs to lows to be greater than 1 at 7/8 and less than 1 at 1/8.