We define the pref-complete semantics for the Preference-Based Argumentation Frameworks (PAFs) of Amgoud and Vesic. The new semantics generalizes Dung’s complete semantics for Argumentation Frameworks (AFs) in the same way that their original semantics (called pref-grounded, pref-stable, pref-preferred) respectively generalize the grounded, stable and preferred semantics for AFs. Additionally, we show that the pref-grounded/stable/preferred semantics are particular cases of the newly defined pref-complete semantics, therefore preserving the semantic hierarchy observed for AF semantics. This yields new ways for computing the semantics of PAFs, since the particular cases can be obtained from the pref-complete semantics with straightforward operations. Our contributions reinforce their thesis of backwards compatibility towards Dung’s AF semantics.