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At certain voltages, using an analogy with gaseous discharges, aqueous-based conduction cells enter a conduction phase that can be described as an avalanche, in which the current rises unbounded, which is limited by the power supply, and electrolysis becomes an irreversible process. This type of conduction is attained at certain voltages depending on the conduction properties of the electrolyte, the concentrations of the salts, and the pH of the solutions. We have found out that the plasma generated by a high-power laser focused into the bulk of the liquid produces a severe change in this phase; that is, the voltage for which this avalanche is produced decreases in typical cases by more than 30%. There is an evidence that this voltage depends on the anion of the salt in the electrolyte. A description of the experiment is given. We also present results of the changes in the properties of the electrolyte generated after an exposure to the laser-generated plasma.