The problem of increasing the slice resolution of functional MRI (fMRI) images without a loss in signal-to-noise ratio is considered. In standard fMRI experiments, increasing the slice resolution by a certain factor decreases the signal-to-noise ratio of the images with the same factor. For this purpose an adapted EPI MRI acquisition protocol is proposed, allowing one to acquire slice-shifted images from which one can generate interpolated super-resolution images, with an increased resolution in the slice direction. To solve the problem of correctness and robustness of the created super-resolution images from these slice-shifted datasets, the use of discontinuity preserving regularization methods is proposed. Tests on real morphological, synthetic functional, and real functional MR datasets have been performed, by comparing the obtained super-resolution datasets with high-resolution reference datasets. In the morphological experiments the image spatial resolution of the different types of images are compared. In the synthetic and real fMRI experiments, on the other hand, the quality of the different datasets is studied as function of their resulting activation maps. From the results obtained in this study, we conclude that the proposed super-resolution techniques can both improve the signal-to-noise ratio and augment the detectability of small activated areas in fMRI image sets acquired with thicker slices.