  We investigate the Kondo effect in a quantum dot with almost degenerate
spin-singlet and triplet states for an even number of electrons. We show that
the Kondo temperature as a function of the energy difference between the states
Delta reaches its maximum around Delta=0 and decreases with increasing Delta.
The Kondo effect is thus enhanced by competition between singlet and triplet
states. Our results explain recent experimental findings. We evaluate the
linear conductance in the perturbative regime.
