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A tunable Kondo effect has been realized in small quantum dots. A dot can be switched from a Kondo system to a non-Kondo system as the number of electrons on the dot is changed from odd to even. The Kondo temperature can be tuned by means of a gate voltage as a single-particle energy state nears the Fermi energy. Measurements of the temperature and magnetic field dependence of a Coulomb-blockaded dot show good agreement with predictions of both equilibrium and nonequilibrium Kondo effects.