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To resolve quantitative mismatch between measurements and the existing theory, we perform systematic theoretical study of the effects of small uniform strain on the electronic properties of single-wall carbon nanotubes. Applied torsion or uniaxial strain induces structural deformations (shifts of the two sublattices, radial and torsional strains induced by the applied uniaxial strain, e.g.), which lead to significantly weaker impact on electronic properties of the strained tube. This damping is more pronounced for torsion. For instance, in tubes with a chiral angle close to 30°, the band gap change is reduced up to 60%. The dominant attenuating factor is the relative shift of the sublattices along the tube axis, manifesting strong electronic coupling with the longitudinal high-energy Raman mode. Obtained results match better the experimental observation of the shifts of optical transition energies and the gauge factor in carbon nanotube based piezoresistive sensors, giving a base for further device development. © 2015 American Chemical Society.