The complexing capacity of synthetic (0.011 M tartrate in 13.5% ethanol) and real wine (Raimat Abadia) in titrations with added total Zn concentrations up to 0.03 M has been determined following the free Zn concentrations with AGNES (absence of gradients and Nernstian equilibrium stripping) technique. A correction to find the preconcentration factor or gain (Y1) really applied at each one of the ionic strengths reached due to Zn additions along the titration has been applied. The standard implementation of AGNES to real wine led to the observation of two anomalous behaviors: (a) an increasingly negative current in the deposition stage (labeled as “HER” effect) and (b) a minimum in the currents of the stripping stage plot (labeled as the “dip” effect). A practical strategy to apply AGNES avoiding the dip effect has been developed to quantify properly free Zn concentrations. The van den Berg–Ružic–Lee linearization method (assuming the existence of just 1:1 complexes) has been adapted to consider the dilution effect and the ionic strength changes. Aggregated stability constants and total ligand concentrations have been calculated from synthetic and wine titration data. The found complexing capacity in the studied wine (cT,L = 0.0179 ± 0.0007 M) indicates the contribution of ligands other than tartrate (which is confirmed to be the main one).