AbstractStellar spectropolarimetry has become an extremely popular technique during the last decade or two, and has led to major advances in the studies of stellar magnetic fields. Many important discoveries have been made thanks to ultra-precise measurements of very small polarimetric signals, which require very stable instruments and special observing strategies. The so called beam-swapping technique is a well-known polarimetric technique capable of suppressing many spurious signals due to various instrumental effects. However, when one is interested in ultra-high signal-to-noise ratio measurements, observers start to hit various limitations introduced by the instrument, by the atmosphere, and even by the software for data-reduction. These limitations cannot be overcome by the observing strategies, and sources of errors other than photon-noise must be taken into account. Here we discuss the advantages of the beam-swapping technique, and the impact of small instrument and atmospheric instabilities, and how these issues offer an explanation for the origin of the apparently significant observed polarisation signals produced by effects other than those intrinsic to the observed target.