In this study, we demonstrate that for the simultaneous hydrodeoxygenation (HDO) of 1,4-anhydroerythritol a comparable yield of tetrahydrofuran is obtained at half the previously reported H2 pressure. The simultaneous hydrodeoxygenation was conducted using a heterogeneous ReO x –Pd/CeO2 catalyst. An L9 Taguchi design of experiment was enacted to elucidate the temperature, pressure, and catalyst loading effects on the yield of the HDO reaction by testing pressures ranging from 40 to 80 bar H2, temperatures of 100–180 °C, and Re loadings of 2–4 wt %. Our design showed that the yield of this reaction is significantly affected by the reaction temperature only. An L9 Taguchi design was conducted for xylitol simultaneous hydrodeoxygenation with pressures ranging from 5 to 10 bar H2, temperatures of 140–180 °C, and Re loadings of 2–4 wt %. The xylitol design elucidated the direct relation of pressure, and the inverse relation of temperature and catalyst loading, to yield with the optimal reaction condition being 140 °C and 10 bar H2.