An anonymous trading system (FIG. 1) identifies the best bids and offers (QuoteSubmit, FIG. 3) from those counterparties (WS A1a1) with which each party (WS A1b1, WS A1b2, . . . . WSA2a2) is currently eligible to deal, while maintaining the anonymity of the potential counterparty and the confidentiality of any specific credit limitations imposed by the anonymous potential counterparty. To that end, each bid or offer (QuoteSubmit, FIG. 3) for a particular type of financial instrument is prescreened by the system for compatibility with limited credit information (for example, a one bit flag indicating whether a predetermined limit has already been exceeded) and an anonymous "Dealable" price (24,26) is calculated for each of the traders (WS A1b, . . . WS A2a) dealing with that particular financial instrument.