We investigate the physical parameters controlling the low-energy screening in carbon nanotubes via electron energy loss spectroscopy and inelastic X-ray scattering. Two plasmon-like features are observed, one near 9 eV (the so-called π plasmon) and one near 20 eV (the so-called π + σ plasmon). At large nanotube diameters, the π + σ plasmon energies are found to depend on the number of walls and not on the radius or chiral vector. The observed shift with number of walls indicates a change in the strength of the screening and in the effective interaction at inter-atomic distances; thus this result suggests a mechanism for tuning the properties of nanotubes.