Three-dimensional X-ray diffraction has been applied to measure in-situ lattice rotations of individual grains deeply embedded in a 2 mm thick copper sample during 6% elongation. The tensile axis of seven grains initially close to <111> all rotated towards this orientation. This common rotation behaviour indicates a limited influence of grain interaction at low strains. Minor variations in the rotation of the tensile axis did not exceed the spread in the predictions by the classic Sachs and Taylor models.