We investigate the phenomenon of electron-positron pair production from vacuum in the presence of a
strong electric field superimposed by a weak but fast varying pulse which substantially increases the total
particle yield. We employ a nonperturbative numerical technique and perform the calculations beyond the
spatially-uniform-field approximation, i.e., dipole approximation, taking into account the coordinate
dependence of the fast component. The analysis of the main characteristics of the pair-production process
(momentum spectra of particles and total amount of pairs) reveals a number of important features which are
absent within the previously used approximation. In particular, the structure of the momentum distribution
is modified both qualitatively and quantitatively, and the total number of pairs created as well as the
enhancement factor due to dynamical assistance become significantly smaller.