In this paper we propose a solution for coupling the execution of a visual servoing task with a recently developed active Structure from Motion strategy able to optimize online the convergence rate in estimating the (unknown) 3D structure of the scene. This is achieved by suitably modifying the robot trajectory in the null-space of the servoing task so as to render the camera motion 'more informative' w.r.t. the states to be estimated. As a byproduct, the better 3D structure estimation also improves the evaluation of the servoing interaction matrix which, in turn, results in a better closed-loop convergence of the task itself. The reported experimental results support the theoretical analysis and show the benefits of the method.