Recent instrumental developments in imaging polarimetry allow array detectors to reach a polarimetric sensitivity of 1 × 10$^-4$ of the intensity. New instrumental effects appear at these levels of sensitivity and generate spurious polarization signals with amplitudes of up to 5 × 10$^-4$. Here I discuss these effects and present methods to avoid them. Polarized spectra with an rms noise of 6 × 10$^-6$ may then be obtained. Furthermore a method is brought to the reader’s attention that allows polarization measurements at the 1 × 10$^-4$ level with regular array detectors, e.g. in the near-infrared.