Acoustic-resonance and dielectric susceptibility measurements are reported for thin plates of KT_1-xNb_xO₃ (0.02<or=x<or=0.03) crystals. A thickness dependence is observed and discussed in terms of a surface-layer model, where the surface of the plates exhibits both dielectric and elastic properties different from those of the bulk-like centre. Surface layer thicknesses of (15+or-5) mu m are found, independent of temperature from T_c+5 to T_c+270K in a sample with T_c=30K and x=0.02. They are also independent of surface treatment, be it etching, lapping or no treatment at all (in the case of a natural surface). Pinning of dislocations at the surface is proposed as the probable origin of the surface layer, and, from the absence of critical effects, the existence of a polar surface of macroscopic dimension above T_c is excluded.