A system and method for making vehicle originated calls to a telematics service provider or other call center. The method includes identifying a call type associated with a desired wireless communication of speech or data to the call center, and then carrying out one of a number of different call connection processes depending on the call type. For voice channel cellular connections, an in-band modem cellular connection is preferably established in most instances using a connection retry strategy that includes primary, secondary, and possibly tertiary connection attempts each of which utilize at least one of a number of different voice and data call origination processes. The system and method can be carried out in connection with various cellular system technologies, but is especially suited for use with GSM systems.