This paper generalizes previous work on automatic generation control (AGC) gain in a single balancing authority system. In previous work, a control performance standard 1 (CPS1)-compliant AGC gain for a single balancing authority interconnection was proposed, assuming that frequency response can be decoupled from AGC dynamics by widening governor dead bands. However, current practices suggest that widening dead bands may not be a wise course to take as it may deteriorate primary frequency response. This paper formulates sufficient conditions for the adequacy of the joint operation of AGC control and primary frequency response to be consistent with frequency response adequacy. Historical data and a simulation of ERCOT are presented to show numerical results.