We investigate a layered ferroelectret that is based on the same layer sequence as a simple electret microphone. Only one electrically charged polymer film is employed instead of two as in previous tubular-channel ferroelectrets. The design has major advantages such as a reduced number of polymer films to be processed and a reduced amount of expensive electret material, as well as the possibility to choose the polarity of the charged layer for optimal stability. We demonstrate that the piezoelectricity in unipolar Teflon®-fluoroethylenepropylene (FEP) ferroelectrets may be considerably more stable than in otherwise similar bipolar ferroelectrets if the most suitable polarity of the poling/charging voltage and thus also of the trapped electret charge is chosen.