  By means of sequential and cotunneling spectroscopy, we study the tunnel
couplings between metallic leads and individual levels in a carbon nanotube
quantum dot. The levels are ordered in shells consisting of two doublets with
strong- and weak-tunnel couplings, leading to gate-dependent level
renormalization. By comparison to a one- and two-shell model, this is shown to
be a consequence of disorder-induced valley mixing in the nanotube. Moreover, a
parallel magnetic field is shown to reduce this mixing and thus suppress the
effects of tunnel renormalization.
