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

Magnetic-Field Dependence of Tunnel Couplings in Carbon Nanotube Quantum Dots