Absence of gradient and Nernstian equilibrium stripping (AGNES) senses the free ion concentration of Zn(II) in solutions containing different ligands, being unaffected by the lack of reversibility of the Zn2+/Zn0 couple under the conditions assayed. In the presence of oxalate, the determination of [Zn2+] agrees with the stability and solubility constants of this sparingly soluble salt, once the precipitation kinetics are taken into account. Different strategies have been analysed and implemented in order to reduce the preconcentration time with the standard electrode of the polarographic stand (smallest drop radius around 0.141 mm): (i) using a lower preconcentration factor when there is no need of enhanced limit of detection; (ii) splitting the deposition stage into two, with a first potential step under diffusion limited conditions; (iii) the analysis of the chronoamperometric response in the deposition stage allows its duration to be adjusted, especially if non-inert complexes contribute to the arriving flux of metal to the mercury electrode. The two-potential-steps strategy is assessed as the most suitable in a general case.