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