α-Pinene, α-terpineol, and 1,8-cineole are compounds naturally present in essential oils, although their amounts vary from oil to oil. Although several studies have reported their antibacterial and antioxidant effects, there are few reports on the synergistic or antagonistic effects of their combinations. The objective of this study was to investigate the combined antibacterial effect of these three compounds. To our knowledge, this is the first report on the prediction of their optimal combination using the mixture design approach. The experimental antibacterial activity of the α-pinene, α-terpineol, and 1,8-cineole mixtures depended on the proportion of each compound in the mixture and the target strain, with minimum inhibitory concentrations (MIC) ranging from 0.31 to 1.85 mg/mL. Using the increased simplex-centroid mixture design, the mixture containing 0.33% of each molecule proved to be the most effective against and had the lowest MIC values. In addition, α-pinene, α-terpineol, and 1,8-cineole showed significant antioxidant activity against 2,2-picryl-1-hydrazyl radical (DPPH), with IC values of 24.53 ± 0.05, 65.63 ± 0.71, and 63.58 ± 0.01 μg/mL, respectively. Statistical planning and the development of utility profiles of the substance mixtures can predict the optimal composition that will exhibit the highest antibacterial activity against as well as antioxidant properties. Furthermore, the synergistic effect of the mixtures can contribute significantly to their successful use as natural preservatives in various applications.