The use of a two-phase decanter (TwPD) for olive-oil extraction produces wastes and byproducts (a small volume of water from oil washing, olive leaves from the defoliator, and a high moisture pomace which can be destoned) that contain valuable bioactive compounds, such as phenolics and/or triterpenic acids. So far, there is no (water) or limited information (leaves and the destoned pomace fraction) on their content of bioactives, especially triterpenic acids. To contribute to the characterization of such streams from cultivars of international interest, in the present study, samples obtained from five mills from the region of Laconia (from one or two harvests) in Greece, where Koroneiki cv dominates, were screened for phenols and/or triterpenic acids. The leaves and pomace were dried at two temperatures (70 °C and/or 140 °C), and the pomace was also destoned before analysis. The liquid wastes contained low amounts of total (TPC) phenols (<140 mg gallic acid/L), hydroxytyrosol (<44 mg/L), and tyrosol (<33 mg/L). The olive leaves varied widely in TPC (12.8–57.4 mg gallic acid/g dry leaf) and oleuropein (0.4–56.8 mg/g dry leaf) but contained an appreciable amount of triterpenic acids, mainly oleanolic acid (~12.5–31 mg/g dry leaf, respectively). A higher drying temperature (140 vs. 70 °C) affected rather positively the TPC/oleuropein content, whereas triterpenic acids were unaffected. The destoned pomace TPC was 15.5–22.0 mg gallic acid/g dw, hydroxytyrosol 3.9–5.6 mg/g dw, and maslinic 5.5–19.3 mg/g dw. Drying at 140 °C preserved better its bioactive phenols, whereas triterpenic acids were not influenced. The present findings indicate that TwPD streams may have a prospect as a source of bioactives for added-value applications. Material handling, including drying conditions, may be critical but only for phenols.