An interconnected lock for use on a door, where the lock has adjustable offset spacing between a deadbolt and latchbolt. The lock includes first and second shafts for actuating the deadbolt lock mechanism, at different offset spacings. A linkage arm connected to and moveable by the latchbolt actuator is alternately connectable to rotate either the first or second deadbolt-actuating shaft. The linkage arm has first and second upper positions, for alternate connection to rotate the first and second deadbolt-actuating shafts, respectively. Upon operation of the interior actuator, the linkage arm moves the deadbolt along the second axis from the latched to the unlatched position at the same time that the operation of the interior actuator moves the latchbolt along the first axis from the latched to the unlatched position.