Deforming elephants of Q-Fano 3-folds

We study deformations of a pair consisting of a Q-Fano 3-fold X with only terminal singularities and its elephant D epsilon|-K-X|. We prove that, if there exists D epsilon|-K-X| with only isolated singularities, the pair (X, D) can be deformed to a pair consisting of a Q-Fano 3-fold with only quotient singularities and a Du Val elephant. When there are only non-normal elephants, we reduce the existence problem of such a deformation to a local problem around the singular locus of the elephant. We also give several examples of Q-Fano 3-folds without Du Val elephants.