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We present a new approach for the fabrication of electrooptically tunable microring resonators in lithium niobate. Planar optical waveguides for vertical light confinement (Deltan o = 0.17) are produced by fluorine ion implantation. Optical microrings and bus waveguides are then formed by laser lithography masking and Ar+ plasma etching. Electrodes are optically isolated from the optical microrings by a polyvinyl alcohol buffer layer with a high dielectric constant (epsiv ~ 70 at 10 Hz) to improve electrooptic tuning. The microrings with a radius of 80 mu m exhibit optical resonances with a modulation depth of 11 dB, a free spectral range of 2 nm, and an electrooptical tunability of 10 pm/V.