A crossing network that matches buy and sell orders based upon a satisfaction and quantity profile includes a number of trader terminals that can be used for entering orders. The orders are entered in the form of a satisfaction density profile that represents a degree of satisfaction to trade a particular instrument at various (price, quantity) combinations. Typically, each order is either a buy order or a sell order. The trader terminals are coupled to a matching controller computer. The matching controller computer can receive as input the satisfaction density profiles entered at each one of the trading terminals. The matching controller computer matches orders (as represented by each trader's satisfaction density profile) so that each trader is assured that the overall outcome of the process (in terms of average price and size of fill) has maximized the mutual satisfaction of all traders. Typically, the matching process is anonymous. The matching process can be continuous or a batch process, or a hybrid of the two. Unmatched satisfaction density profiles can be used to provide spread and pricing information. Factors other than price and quantity also may be used to determine the degree of satisfaction. Optionally, priority may be given to certain profiles in the matching process to accommodate stock exchange rules, for example, requiring that priority be given to orders exhibiting the best price, regardless of size or any other consideration.