Researchers studying the polarization characteristics of the optical environment prefer to use sequential imaging polarimetry, because it is inexpensive and simple. This technique takes polarization pictures through polarizers in succession. Its main drawback is, however, that during sequential exposure of the polarization pictures, the target must not move, otherwise so-called motion artifacts are caused after evaluation of the polarization pictures. How could these disturbing motion artifacts be minimized? Taking inspiration from photography, our idea was to take the polarization pictures with an exposure that is long enough so that the changes of the moving/changing target can be averaged and, thus, motion artifacts are reduced, at least in a special case when the motion has a stable mean. In the laboratory, we demonstrated the performance of this method when the target was a wavy water surface. We found that the errors of the measured degree and angle of polarization of light reflected from the undulating water surface decreased with increasing exposure time (shutter speed) and converged to very low values. Although various simultaneous polarimeters (taking the polarization pictures at once) are available that do not suffer from motion artifacts, our method is much cheaper and performs very well, at least when the target is a wavy water surface.