A control strategy for a pressurized water nuclear reactor that employs separate, independent control rod banks for respectively controlling Tavg and axial offset within corresponding deadbands. The strategy does not permit the control banks controlling reactor core power and the control banks controlling axial offset to move together, but normally gives preference to the control banks controlling the Tavg except when a demand signal is received simultaneously by both independent control rod banks to move in a same direction, in which case, the control bank compensating for the axial offset is given preference.