Additional instructions in support of 24/31-bit addressing include two new register-register call/return instructions which also effect an addressing mode change (e.g. Branch and Save and Set Mode, BASSM, the 24/31 bit version of a call where the linkage address including the mode is saved and a branch is taken to an address in a possibly different mode, and BSM, Branch and Set Mode, the 24/31 bit version of a return, where the return is directly to the previously saved linkage address and in its previous mode). Taken together, BASSM and BSM allow 24-bit calls to 31-bit (and return to 24-bit), 31-bit calls to 24-bit (and return to 31-bit), 24-bit calls to 24-bit (and return to 24-bit) and 31-bit calls to 31-bit (and return to 31-bit).