Conductivity imaging based on the current-injection MRI technique has been developed in magnetic resonance electrical impedance tomography. Current injected through a pair of surface electrodes induces a magnetic flux density distribution inside an imaging object, which results in additional magnetic field inhomogeneity. We can extract phase changes related to the current injection and obtain an image of the induced magnetic flux density. Without rotating the object inside the bore, we can measure only one component B_z of the magnetic flux density B = (B_x, B_y, B_z). Based on a relation between the internal conductivity distribution and B_z data subject to multiple current injections, one may reconstruct cross-sectional conductivity images. As the image reconstruction algorithm, we have been using the harmonic B_z algorithm in numerous experimental studies. Performing conductivity imaging of intact animal and human subjects, we found technical difficulties that originated from the MR signal void phenomena in the local regions of bones, lungs and gas-filled tubular organs. Measured B_z data inside such a problematic region contain an excessive amount of noise that deteriorates the conductivity image quality. In order to alleviate this technical problem, we applied hybrid methods incorporating ramp-preserving denoising, harmonic inpainting with isotropic diffusion and ROI imaging using the local harmonic B_z algorithm. These methods allow us to produce conductivity images of intact animals with best achievable quality. We suggest guidelines to choose a hybrid method depending on the overall noise level and existence of distinct problematic regions of MR signal void.