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Complex absorbing potentials (CAPs) are artificial potentials added to electronic Hamiltonians to make the wavefunction of metastable electronic states square-integrable. This makes the electronic structure problem of electronic resonances comparable to that of electronic bound states, thus reducing the complexity of the problem. CAPs depend on two types of parameters: the coupling parameter $η$ and a set of spatial parameters which define the onset of the CAP. It has been a common practice over the years to minimize the CAP perturbation on the physical electronic Hamiltonian by running an $η-$trajectory, whereby one fixes the spatial parameters and varies $η$. The optimal $η$ is chosen according to the minimum log-velocity criterion. But the effectiveness of an $η-$trajectory strongly depends on the values of the fixed spatial parameters. In this work, we propose a more general criterion, called the $ξ-$criterion, which allows one to minimize any CAP parameter, including the CAP spatial parameters. Indeed, we show that fixing $η$ and varying the spatial parameters according to a scheme (i.e., running a spatial trajectory) is a more efficient and reliable way of minimizing the CAP perturbations (which is assessed using the $ξ-$criterion). We illustrate the method by determining the resonance energy and width of the temporary anion of dinitrogen, at the Hartree-Fock and EOM-EA-CCSD levels, using two different types of CAPs: the box- and the smooth Voronoi-CAPs.