According to certain embodiments of the present invention, cryptosynchronization values are calculated on an initiating and/or responding device in a communications system such that cryptosynchronization-based procedures might succeed even when the discrepancy between the system times of the initiating and responding devices exceeds the cryptosync constraints imposed by the communications system. In one embodiment, the initiating device add/subtracts a cryptosynchronization adjustment value x to/from the initiating device's system time to yield an adjusted initiator cryptosynchronization value. In another embodiment, the receiving device adjusts the receiving device's system time to yield an adjusted receiver cryptosynchronization value.