  The concept of the "Kondo box" describes a single spin, antiferromagnetically
coupled to a quantum dot with a finite level spacing. Here, a Kondo box is
formed in a carbon nanotube interacting with a localized electron. We
investigate the spins of its first few eigenstates and compare them to a recent
theory. In an 'open' Kondo-box, strongly coupled to the leads, we observe a
non-monotonic temperature dependence of the nanotube conductance, which results
from a competition between the Kondo-box singlet and the 'conventional' Kondo
state that couples the nanotube to the leads.
