  We study a refrigerator model which consists of two $n$-level systems
interacting via a pulsed external field. Each system couples to its own thermal
bath at temperatures $T_h$ and $T_c$, respectively ($\theta\equiv T_c/T_h<1$).
The refrigerator functions in two steps: thermally isolated interaction between
the systems driven by the external field and isothermal relaxation back to
equilibrium. There is a complementarity between the power of heat transfer from
the cold bath and the efficiency: the latter nullifies when the former is
maximized and {\it vice versa}. A reasonable compromise is achieved by
optimizing over the inter-system interaction and intra-system energy levels the
product of the heat-power and efficiency. The efficiency is then found to be
bounded from below by $\zeta_{\rm CA}=\frac{1}{\sqrt{1-\theta}}-1$ (an analogue
of Curzon-Ahlborn efficiency for refrigerators), besides being bound from above
by the Carnot efficiency $\zeta_{\rm C} = \frac{1}{1-\theta}-1$. The lower
bound is reached in the equilibrium limit $\theta\to 1$, while the Carnot bound
is reached (for a finite power and a finite amount of heat transferred per
cycle) in the macroscopic limit $\ln n\gg 1$. The efficiency is exactly equal
to $\zeta_{\rm CA}$, when the above optimization is constrained by assuming
homogeneous energy spectra for both systems.
