Consider the problem of controlling an unstable process while using as little information as possible. There is a fundamental trade--off between the amount of information used per sample and the controller's performance. Indeed, very recently, Kostina \emph{et al.} 2022 considered the specific case of an unstable AR(1) process with bounded noise in $[-B, B]$ and showed that with a fixed rate per sample control, an unstable process with a gain $\alpha>1$ has a fundamental limit of $\lfloor \alpha \rfloor + 1$ quantization levels per sample. E.g., with $1 < \alpha < 2$, there is a fundamental limit of $1$ bit per sample. We revisit the problem assuming an average rate per sample constraint. We show that not only the $1$ bit per sample bound is pessimistic, one can control an unstable AR(1) process at a negligible rate for reasonable $\alpha$, with a simple \emph{interleaved application of a 1--bit quantizer}. In this case, we derive a new converse result for average rate control and show it is much lower than that with a fixed rate. The achievable scheme we suggest asymptotically matches the lower bound. We give a practical and simple controller with a bit--rate close to the theoretical limit shown in \cite{zhang2006data}. For example, with $\alpha = 1 + \epsilon$, we prove that a rate of $\log_2(1+\epsilon) = \frac{\epsilon}{\ln(2)} + O(\epsilon^2)$ bits per sample is necessary, yet a rate $\frac{1}{\lfloor \frac{\ln(2)}{\epsilon}\rfloor}$ is achievable.