A process is provided that allows an exportable SSL client to negotiate an encrypted session using strong encryption with a server if the server is allowed to use strong encryption. With this process, the SSL client is normally limited to export strength encryption. But, when it is communicating with an approved server, it is able to expand the available set of encryption algorithms to include stronger algorithms/key lengths. The process involves performing an SSL handshake twice. The process begins when a client, i.e. a user, wants to establish a session with a server. The client first initiates a network connection to the server. The first handshake between an export client and an approved server results in an SSL session that uses export strength encryption. This establishes a connection using an exportable cipher suite. The client examines the server's certificate obtained as part of the first handshake. If the server is not approved, the SSL session transfers application data that are protected by the export cipher. If the server is approved, then the client initiates a second handshake, this time allowing stronger cipher suites. The result of the second handshake is an SSL session that uses strong encryption. The SSL session may then be used to transfer application data that are protected by the strong cipher suite. At this point, the process is complete.