In this paper we present new experiments on the switching of the polarization in thin (< 1 ~tm) ferroelectric copolymer films of P(VDF-TrFE). We observed an unexpectedly short switching time for these thin films: The polarization of a 0.2 ~tm thick film could be reversed by poling fields of 600MV/m in less than lOOns. This result which may revive interest in ferroelectric data storage is discussed in terms of a switching process which also involves the ohmic conductivity of the sample.