In the context of video editing, enforcing spatio-temporal consistency is an important issue. With that purpose, the current varia- tional models for gradient domain video editing include space and time regularization terms. The spatial terms are based on the usual space derivatives, the temporal ones are based on the convective derivative, and both are balanced by a parameter . However, the usual discretiza- tions of the convective derivative limit the value of to a certain range, thus limiting these models from achieving their full potential. In this paper, we propose a new numerical scheme to compute the convective derivative, the deblurring convective derivative, which allows us to lift this constraint. Moreover, the proposed scheme introduces less errors than other discretization schemes without adding computational com- plexity. We use this scheme in the implementation of two gradient do- main models for temporally consistent video editing, based on Poisson and total variation type formulations, respectively. We apply these mod- els to three video editing tasks: inpainting correction, object insertion and object removal.