  We study a quantum dot connected to the bulk by single-mode junctions at
almost perfect conductance. Although the average charge $e\langle N \rangle$ of
the dot is not discrete, its spin remains quantized: $s=1/2$ or $s=0$,
depending (periodically) on the gate voltage. This drastic difference from the
conventional mixed-valence regime stems from the existence of a broad-band,
dense spectrum of discrete levels in the dot. In the doublet state, the Kondo
effect develops at low temperatures. We find the Kondo temperature $T_K$ and
the conductance at $T\lesssim T_K$.
