Producing wines within an acceptable range of astringency is important for quality and consumer acceptance. Astringency can be modified by fining during the winemaking process and the use of vegetable proteins (especially potato proteins) as fining agents has gained increasing interest due to consumers’ requirements. The research presented was the first to investigate the effect of a potato protein dose on the kinetics of tannin and phenolic removal compared to gelatin for two unfined Cabernet Sauvignon wines. To further understand the results, the influence of the wine matrix and fining parameters (including pH, ethanol concentration, sugar concentration, temperature, and agitation) were tested according to a fractional 25-1 factorial design on one of the Cabernet Sauvignon wines using potato proteins. The results from the factorial design indicate that potato protein fining was significantly influenced by wine pH, ethanol concentration, fining temperature as well as an interaction (pH × ethanol) but not by sugar content or agitation. Insights into the steps required for the optimisation of fining were gained from the study, revealing that potato protein fining efficiency could be increased by treating wines at higher temperatures (20 ◦C, rather than the conventional 10–15 ◦C), and at both a lower pH and/or alcohol concentration. © 2019 by the authors.