1. A method for facilitating trading of securities over a computer system, comprising the steps of: electronically receiving a first buy or sell order for a security from a first user; determining that said first order is reasonably priced; transmitting to a second user an electronic notification that a reasonably priced order for said security is present, but without notifying said second user of the side of said first order; receiving a second order from said second user, wherein said second order is a contra to said first order and sufficiently aggressive in price to cross said first order; and executing a trade comprising said first order and said second order at said first order's limit.