We consider the well-known 4D-VAR problem in data assimilation and present some new techniques for handling the solution of the involved subproblem. The problem is first briefly reviewed, and the relation of the standard method with the nonlinear Gauss-Newton algorithm recalled, including the need of its globalization (for instance using a trust-region technique). The solution of the subproblem is then considered and it is shown how this solution may be viewed (and economically computed) in the dual space. The strategy is then applied to the GLTR technique for trust-regions. The problem of loss of symmetry is discussed with a tentative solution. Some results are finally presented for MATLAB experiments, but also for versions implemented in the NEMOVAR and ROMS systems.