While in the paralectric phase of ferroelectrics, and in centrosymmetric materials in general, the dielectric tunability is symmetrical for positive and negative electric bias fields, in noncentrosymmetric materials this is not the case. By using the thermodynamic theory, and tetragonal phase of monodomain single-crystal perovskites BaTiO3 and Pb(Zr,Ti)O-3, as examples, we show that the theoretical tunability region of ferroelectrics may, in principle, be considerably broadened and tunability greatly enhanced by applying electric-bias field antiparallel to polarization. Available experimental data are in qualitative agreement with the theoretical predictions. (c) 2006 American Institute of Physics.