Retentive (memory-utilizing) sensing-acting agents, when they are distributed or power-constrained, often operate under limitations on the communication between their sensing, memory and acting components. This requires them to trade off the external cost that they incur with the capacity of their communication channels, which translates into the sequential rate-distortion problem of minimizing the rate of information required for the controller’s operation, under a constraint on its external cost. In this paper we formulate this problem with a simple information term, by viewing the memory reader as one more sensor, and the memory writer as one more actuator. This allows us to reduce the bounded retentive control problem to the memoryless one, studied in Part I of this work. We further investigate the form of the resulting optimal solution, and demonstrate its interesting phenomenology.